Sr Examen
Integral de (x^3*cosx/2+1/2)sqrt/4-x^2 dx
Solución
Ha introducido
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2 / | | // 3 \ \ | ||x *cos(x) 1| ___ | | ||--------- + -|*\/ x | | |\ 2 2/ 2| | |--------------------- - x | dx | \ 4 / | / -2
$$\int\limits_{-2}^{2} \left(- x^{2} + \frac{\sqrt{x} \left(\frac{x^{3} \cos{\left(x \right)}}{2} + \frac{1}{2}\right)}{4}\right)\, dx$$
Integral((((x^3*cos(x))/2 + 1/2)*sqrt(x))/4 - x^2, (x, -2, 2))
Respuesta (Indefinida)
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/ | / / ___ ___\ / ___ ___\ \ / ___ ___\ | // 3 \ \ | |\/ 2 *\/ x | 4 |\/ 2 *\/ x | | ___ ____ 4 |\/ 2 *\/ x | | ||x *cos(x) 1| ___ | | 4725*C|-----------|*Gamma(1/4) 45*x *C|-----------|*Gamma(1/4) | \/ 2 *\/ pi *x *C|-----------| | ||--------- + -|*\/ x | 3 3/2 | | ____ | | ____ | ___ 5/2 ___ 7/2 ___ 3/2 ___ ___ | | ____ | | |\ 2 2/ 2| x x ___ ____ | \ \/ pi / \ \/ pi / 315*\/ 2 *x *cos(x)*Gamma(1/4) 45*\/ 2 *x *Gamma(1/4)*sin(x) 1575*\/ 2 *x *Gamma(1/4)*sin(x) 4725*\/ 2 *\/ x *cos(x)*Gamma(1/4)| \ \/ pi / | |--------------------- - x | dx = C - -- + ---- - \/ 2 *\/ pi *|- ------------------------------ + ------------------------------- - -------------------------------- - ------------------------------- + --------------------------------- + ----------------------------------| + ------------------------------ | \ 4 / 3 12 | 8192*Gamma(13/4) 512*Gamma(13/4) ____ ____ ____ ____ | 8 | \ 2048*\/ pi *Gamma(13/4) 1024*\/ pi *Gamma(13/4) 4096*\/ pi *Gamma(13/4) 8192*\/ pi *Gamma(13/4) / /
$$\int \left(- x^{2} + \frac{\sqrt{x} \left(\frac{x^{3} \cos{\left(x \right)}}{2} + \frac{1}{2}\right)}{4}\right)\, dx = C + \frac{x^{\frac{3}{2}}}{12} + \frac{\sqrt{2} \sqrt{\pi} x^{4} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)}{8} - \frac{x^{3}}{3} - \sqrt{2} \sqrt{\pi} \left(- \frac{45 \sqrt{2} x^{\frac{7}{2}} \sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{1024 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} - \frac{315 \sqrt{2} x^{\frac{5}{2}} \cos{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{2048 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{1575 \sqrt{2} x^{\frac{3}{2}} \sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{4096 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{4725 \sqrt{2} \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{8192 \sqrt{\pi} \Gamma\left(\frac{13}{4}\right)} + \frac{45 x^{4} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{512 \Gamma\left(\frac{13}{4}\right)} - \frac{4725 C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8192 \Gamma\left(\frac{13}{4}\right)}\right)$$
Respuesta numérica
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(-5.14038347943263 + 0.277889429944293j)
(-5.14038347943263 + 0.277889429944293j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.