Question

Evaluate each definite integral. Enter either an exact answer or an answer rounded to three decimal places. (a) $$ \int_{1}^{4} (96x^{-3} - 10x + 4)dx = $$ (b) $$ \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (8 \sin t + 8 \csc^2 t)dt = $$

Name: evaluate each definite integral enter either an exact answer or an answer rounded to three decimal places a int14 96x 3 10x 4dx b intfracpi4fracpi2 8 sin t 8 csc2 tdt 11278
Uploaded: 2024-07-01T23:10:20-08:00
Duration: 4 min 14 s
Channel: Vincenzo Zaccaro
Description: evaluate each definite integral enter either an exact answer or an answer rounded to three decimal places a int14 96x 3 10x 4dx b intfracpi4fracpi2 8 sin t 8 csc2 tdt 11278

          Evaluate each definite integral. Enter either an exact answer or an answer rounded to three decimal places.
(a) $$ \int_{1}^{4} (96x^{-3} - 10x + 4)dx = $$
(b) $$ \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (8 \sin t + 8 \csc^2 t)dt = $$

$evaluate each definite integral enter either an exact answer or an answer rounded to three decimal places a int14 96x 3 10x 4dx b intfracpi4fracpi2 8 sin t 8 csc2 tdt 11278$

Added by Adrian K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

07/01/2024

Step 1

The antiderivative of $96x^{-3}$ is $96 \frac{x^{-3+1}}{-3+1} = 96 \frac{x^{-2}}{-2} = -48x^{-2}$. The antiderivative of $-10x$ is $-10 \frac{x^{1+1}}{1+1} = -10 \frac{x^2}{2} = -5x^2$. The antiderivative of $4$ is $4x$. So, the antiderivative $F(x)$ is: $$ F(x) = Show more…

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Evaluate each definite integral. Enter either an exact answer or an answer rounded to three decimal places. (a) $$ \int_{1}^{4} (96x^{-3} - 10x + 4)dx = $$ (b) $$ \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (8 \sin t + 8 \csc^2 t)dt = $$