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f(x)=xsin(3x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫0π(xsin⁡(3x))dx\int_0^{\pi}\left(x\sin\left(3x\right)\right)dx

Step-by-step Solution

Learn how to solve integrals involving logarithmic functions problems step by step online. Integrate the function xsin(3x) from 0 to pi. We can solve the integral \int x\sin\left(3x\right)dx 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. Solve the integral to find v.
Integrate the function xsin(3x) from 0 to pi

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Final answer to the exercise

π−13cos⁡(3π)−0⋅(−13)cos⁡(3⋅0)+19sin⁡(3π)\pi -\frac{1}{3}\cos\left(3\pi \right)- 0\cdot \left(-\frac{1}{3}\right)\cos\left(3\cdot 0\right)+\frac{1}{9}\sin\left(3\pi \right)

Try other ways to solve this exercise

  • Choose an option
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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∫0π(xsin(3x))dx
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