Evaluate the following iterated integrals. int_1^3int_0^{pi/2}xsin y dy dx

Evaluate the following iterated integrals. int_1^3int_0^{pi/2}xsin y dy dx

Question
Integrals
asked 2021-01-08
Evaluate the following iterated integrals.
\(\int_1^3\int_0^{\pi/2}x\sin y\ dy\ dx\)

Answers (1)

2021-01-09
\(\text{We have to evaluate the integral }\)
\(\int_1^3\int_0^{\pi/2}x\sin y\ dy\ dx\)
\(\int_1^3 x(\int_0^{\pi/2}\sin y\ dy)dx\)
\(\int_1^3 x[-\cos y]_0^{\pi/2}dx\)
\(-\int_1^3 x(0-1)dx\)
\(\int_1^3 xdx\)
\([\frac{x^2}{2}]_1^3\)
\(=\frac{9}{2}-\frac{1}{2}\)
\(=\frac{8}{2}\)
\(=4\)
\(\text{therefore}\)
\(\int_1^3\int_0^{\pi/2}x\sin y\ dy\ dx=4\)
0

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