Calculus Archive: Questions from March 30, 2023
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2. \( \left(5\right. \) pts ) Evaluate \( \left.\int_{-2}^{2} \int_{-4}^{4} \int_{0}^{\sqrt{4-y^{2}}} \int_{\left(1+x^{2}+y^{2}\right)^{3}} d x d z d y\right) \)2 answers -
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Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ f(x, y)=11 y \sqrt{x+2} \] \[ \int_{0}^{2} f(x, y) d x= \] \[ \int_{0}^{3} f(x, y) d y= \]2 answers -
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1) Evalúa la integral usando la formula de integracion por partesisimplificala respuesta. ( \( \left.\int u d v=u v-\int v d u\right) \) \[ \int_{0}^{\pi} x \sin x d x \]2 answers -
) Resuelve usando integración tabular por partes, y luego simplifica. \[ \int\left(x^{2}-1\right) e^{x} d x \]2 answers -
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7) Resuelve usando sustitución trigonométrica y simplifica. \[ \int \frac{1}{\sqrt{4 x^{2}+1}} d x \]2 answers -
9) Resuelve la inte gral \( \int \frac{1}{\left(x^{2}+1\right)^{2}} d x ; y \) luego simplifica la respuesta.2 answers -
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find dy/dx for both please!
(iii) \( \quad y=\sin x^{2}+\sin ^{2} x \) (iv) \( y=\frac{4 x^{3}-x}{x^{2}+5 x} \)2 answers -
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Find \( y^{\prime} \) for \( y=y(x) \) defined implicitly by \( 3 x y-x^{2}-4=0 \). A. \( y^{\prime}=\frac{3 x-2 y}{4} \) B. \( y^{\prime}=\frac{2}{3} x \) C. \( y^{\prime}=\frac{3 y-2 x}{3 x} \) D. \2 answers -
como es el procedimiento del la tabla de integrales
\( I=\int \frac{\sec ^{2} \theta \tan ^{2} \theta}{\sqrt{9-\tan ^{2} \theta}} d \theta \)2 answers -
\( 7: \) If \( \iiint_{E} f(x, y, z) d V=\int_{0}^{\pi / 2} \int_{0}^{\pi / 4} \int_{0}^{\cos (\theta)} 18 \rho^{2} \sin (\phi) \cos (\phi) d \rho d \theta d \phi \), find \[ f(x, y, z)= \]2 answers -
PLEASE do problem 1,5,9, and17 and show steps.
In Exercises 1-30, find the general solution of the given equation. 1. \( y^{\prime \prime}-y^{\prime}-12 y=0 \) 2. \( 3 y^{\prime \prime}-y^{\prime}=0 \) 3. \( y^{\prime \prime}+3 y^{\prime}-4 y=0 \)2 answers -
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If \( y=\cos \left(\frac{\pi}{2} f(t)\right), f(0)=1 \) and \( f^{\prime}(0)=2 \), then find \( y^{\prime} \) at \( t=0 \). a. 1 b. \( -\frac{\pi}{2} \) c. \( -\pi \) d. -12 answers -
#13 & #19 please
In Exercises 11-20, find the volume of the solid generated by revolving the region bounded by the lines and curves about the \( x \)-axis. 11. \( y=x^{2}, \quad y=0, \quad x=2 \) 12. \( y=x^{3}, \quad2 answers -
with steps plz
Calculate \( y^{\prime} \). \[ y=7 \ln \left(x^{2} e^{x}\right) \] \[ y^{\prime}=x \ln 2 x+x^{2} \] \[ y^{\prime}=3 x^{2} \] \[ y^{\prime}=\frac{2 e^{x}+x \ln x^{2}}{x} \] \[ y^{\prime}=7\left(\frac{22 answers -
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