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Exercise

∫π4π2−9xcsc2xdx\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}-9xcsc^2xdx

Step-by-step Solution

Learn how to solve problems step by step online. Integrate the function -9xcsc(x)^2 from pi/4 to pi/2. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int x\csc\left(x\right)^2dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.
Integrate the function -9xcsc(x)^2 from pi/4 to pi/2

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Final answer to the exercise

−9π4+9ln⁡(12)\frac{-9\pi }{4}+9\ln\left(\frac{1}{\sqrt{2}}\right)

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  • Integrate by partial fractions
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  • Integrate using tabular integration
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  • Integrate using basic integrals
  • Product of Binomials with Common Term
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∫π4 π2 −9xcsc2xdx
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