Use the indicated substitution to evaluate the integral. \int_0^2 {\frac{{{x^2}}}{{\sqrt {16 -...


Use the indicated substitution to evaluate the integral.

{eq}\int_0^2 {\frac{{{x^2}}}{{\sqrt {16 - {x^2}} }}dx, \quad x = 4\sin \theta } {/eq}

Definite Integral:

The integral in which the value of the boundaries of the limits are given, and the resulting value is fixed is known as the definite integral. We will use the substitution method to solve this question.

Answer and Explanation: 1

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$$I=\int_{0}^{2}\dfrac{x^{2}}{\sqrt{16-x^{2}}}\text{ d}x $$

Let {eq}x=4\sin(\theta) {/eq}. Differentiate with respect to...

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Evaluating Definite Integrals Using the Fundamental Theorem


Chapter 16 / Lesson 2

In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.

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