Evaluate the integral.
-$$\int _ { \pi / 4 } ^ { 3 \pi / 4 } 9 \csc ^ { 2 } x d x$$
A) 18
B) 9
C) 0
D) -18

Name: Evaluate the integral. -\[\int _ { \pi / 4 } ^ { 3 \pi / 4 } 9 \csc ^ { 2 } x d x\] A) 18 B) 9 C) 0 D) -18
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Question

Quizplus · Accepted Answer

The integral of $\csc^2 x$ is $-\cot x$. Evaluating from $\pi/4$ to $3\pi/4$, we get $-\cot(3\pi/4) + \cot(\pi/4)$, which simplifies to $1 + 1 = 2$. Multiplying by 9 gives 18.

Evaluate the Integral ∫π/43π/49csc⁡2xdx\int _ { \pi / 4 } ^ { 3 \pi / 4 } 9 \csc ^ { 2 } x d x∫π/43π/4​9csc2xdx

Evaluate the Integral $\int _ { \pi / 4 } ^ { 3 \pi / 4 } 9 \csc ^ { 2 } x d x$