Evaluate: {eq}\displaystyle \int_{\frac{\pi}{2}}^{\pi} \int_{0}^{x^2} \frac{1}{x} \cos \left( \frac{y}{x} \right) \mathrm{d}y\ \mathrm{d}x {/eq}.
Question:
Evaluate: {eq}\displaystyle \int_{\frac{\pi}{2}}^{\pi} \int_{0}^{x^2} \frac{1}{x} \cos \left( \frac{y}{x} \right) \mathrm{d}y\ \mathrm{d}x {/eq}.
Double Integration:
The process of integration can be implemented multiple times, which is called iterated integration. This can be done over multiple variables for expressions that contain more than one independent variable. The order to which variable we would be integrating is indicated by the order of the differential terms of the integrand.
Answer and Explanation:
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View this answerWe evaluate the iterated integral. We do this by iteratively implementing the integral first with respect to y and then with respect to x as indicated...
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Chapter 12 / Lesson 15Understand what a double integral is and what the rules for double integration are. Learn different uses for double integrals, and practice evaluating double integrals by following examples.