Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate using trigonometric identities
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Rewrite the integrand $\left(\sin\left(x\right)-2\right)^2$ in expanded form
Learn how to solve definite integrals problems step by step online.
$\int_{0}^{\pi }\left(\sin\left(x\right)^2-4\sin\left(x\right)+4\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (sin(x)-2)^2 from 0 to pi. Rewrite the integrand \left(\sin\left(x\right)-2\right)^2 in expanded form. Expand the integral \int_{0}^{\pi }\left(\sin\left(x\right)^2-4\sin\left(x\right)+4\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Reduce \sin\left(x\right)^2 by applying trigonometric identities. The integral \int_{0}^{\pi }\frac{1-\cos\left(2x\right)}{2}dx results in: \frac{\pi}{2}.