Question

(1.8) $$ \int_{0}^{\sqrt{\frac{\pi}{4}}} (\sin 2x^2)^2 x \cos 2x^2 dx $$ (1.9) $$ \int \frac{3(e^2)^2}{(e^x)^2 + e^x - 2} dx, x > 0 $$

Name: 18 int0sqrtfracpi4 sin 2x22 x cos 2x2 dx 19 int frac3e22ex2 ex 2 dx x 0 69688
Uploaded: 2025-07-01T13:47:31-08:00
Duration: 5 min 38 s
Channel: Sam Stansfield
Description: 18 int0sqrtfracpi4 sin 2x22 x cos 2x2 dx 19 int frac3e22ex2 ex 2 dx x 0 69688

          (1.8) $$ \int_{0}^{\sqrt{\frac{\pi}{4}}} (\sin 2x^2)^2 x \cos 2x^2 dx $$
(1.9) $$ \int \frac{3(e^2)^2}{(e^x)^2 + e^x - 2} dx, x > 0 $$

$18 int0sqrtfracpi4 sin 2x22 x cos 2x2 dx 19 int frac3e22ex2 ex 2 dx x 0 69688$

Added by Christine C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

07/01/2025

Step 1

8), we need to evaluate the definite integral: $$ I = \int_{0}^{\sqrt{\frac{\pi}{4}}} (\sin 2x^2)^2 x \cos 2x^2 dx $$ Let's use a substitution. Let $u = \sin 2x^2$. Then, we need to find $du$. $$ \frac{du}{dx} = \frac{d}{dx}(\sin 2x^2) $$ Using the chain rule, Show more…

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