Evaluate {eq}\int_0^{\pi/2} (2-\sin\theta)^2 \ d\theta {/eq}


Evaluate {eq}\int_0^{\pi/2} (2-\sin\theta)^2 \ d\theta {/eq}

Evaluate the Integral:

Let us assume that {eq}f(x) {/eq} is the function of {eq}x {/eq} and we want to find a integral of {eq}f(x) . {/eq} To find this integral we need to find the anti-derivative of {eq}f(x) {/eq} with respect to {eq}x {/eq} using the following integral formula.

{eq}\displaystyle\int \cos \left(u\right)du=\sin \left(u\right)\\ \displaystyle\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1 {/eq}

Answer and Explanation: 1

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Consider the integral

{eq}\displaystyle\int_0^{\pi/2} (2-\sin\theta)^2 \ d\theta\\ \displaystyle=\int _0^{\frac{\pi }{2}}\left (4-4\sin \left(\theta...

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Using Integration By Parts


Chapter 13 / Lesson 7

Learn how to use and define integration by parts. Discover the integration by parts rule and formula. Learn when and how to use integration by parts with examples.

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