Integració/Per parts Per parts Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8747;«/mo»«/math»#func2 dx

Recordeu que les funcions trigonomètriques són: sin(), cos(), tan(), asin(), acos(), atan() i que l'exponent de la funció Wiris el posa sobre el parèntesi de l'argument:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mo»(«/mo»«mi»x«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math», no com ho fem a classe «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»sin«/mi»«mn»2«/mn»«/msup»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math». Si volem posar només l'argument al quadrat posarem: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sin«/mi»«mo»(«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>[</mo><mi>p</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>p</mi><mo>,</mo><mo>&nbsp;</mo><mi>exp</mi><mo>(</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>exp</mi><mo>(</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>d</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mo>[</mo><mi>exp</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>sin</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>cos</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>atan</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mo>(</mo><mi>ln</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>^</mo><mi>f</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mo>[</mo><mi>sin</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>cos</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>p</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L3</mi><mo>=</mo><mo>[</mo><mi>asin</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>acos</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mo>(</mo><mi>ln</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>^</mo><mi>f</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>&lt;</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><msub><mi>L</mi><mi>e</mi></msub><mo>*</mo><msub><mi>L1</mi><mi>g</mi></msub></mtd></mtr></mtable><mrow><mi>e</mi><mo>&lt;</mo><mn>6</mn></mrow><mtable><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><msub><mi>L</mi><mi>e</mi></msub><mo>*</mo><msub><mi>L2</mi><mi>g</mi></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><msub><mi>L</mi><mi>e</mi></msub><mo>*</mo><msub><mi>L3</mi><mi>g</mi></msub></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>func2</mi><mo>=</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>∫</mo><mi>h</mi><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integració/Quasiinmediata Quasiimmediates Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8747;«/mo»«/math»(#func2) dx

Encara que apliqueu la fórmula del logaritme, NO poseu valor absolut ni poseu cap lletra per a la constant.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>s</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>^</mo><mn>2</mn><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>rr</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>s</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>^</mo><mi>s</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>asin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>atan</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>tan</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msup><exponentiale/><mi>x</mi></msup><mo>,</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>asin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>atan</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>tan</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><msup><exponentiale/><mi>x</mi></msup><mo>,</mo><mi>ln</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>g</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></mtd></mtr></mtable></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><mi>atan</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>func2</mi><mo>=</mo><mi>simplificar</mi><mo>(</mo><apply><diff/><bvar><mi>x</mi></bvar><mi>sol</mi></apply><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>6</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nota</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><apply><diff/><bvar><mi>x</mi></bvar><mrow><mo>(</mo><mi>sol</mi><mo>-</mo><mi>y</mi><mo>)</mo></mrow></apply><mo>=</mo><mn>0</mn><mo>)</mo><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>↦</mo><mfenced><mrow><mi>x</mi><mi>sol</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>0</mn><mo>?</mo></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer><correctAnswer id="3"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">nota</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Integració/Racionals Arrels reals (barreja) Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8747;«/mo»«/math»#func2 dx