Question

5. \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^5 \theta \ d\theta 6. \int_0^{2\pi} \sin^2(\frac{1}{3}\theta) \ d\theta 7. \int_0^{\frac{\pi}{2}} \cos^5 x \ dx 8. \int_0^a \frac{dx}{(a^2+x^2)^{\frac{3}{2}}}, \quad a>0.

          5. \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^5 \theta \ d\theta
6. \int_0^{2\pi} \sin^2(\frac{1}{3}\theta) \ d\theta
7. \int_0^{\frac{\pi}{2}} \cos^5 x \ dx
8. \int_0^a \frac{dx}{(a^2+x^2)^{\frac{3}{2}}}, \quad a>0.

5. ∫0^(π)/(2) sin^7 θcos^5 θ dθ6. ∫0^2π sin^2((1)/(3)θ) dθ7. ∫0^(π)/(2) cos^5 x dx
8. ∫0^a (dx)/((a^2+x^2)^(3)/(2)), a>0.

Added by Jamie C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/23/2023

Step 1

Step 1: For the first integral, we can use the trigonometric identity $\sin^2\theta = 1 - \cos^2\theta$ to simplify the integrand. Show more…

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