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Exercise

$\int_0^{\pi}\cos\left(3x\right)dx$

Step-by-step Solution

1

Apply the formula: $\int\cos\left(ax\right)dx$$=\frac{1}{a}\sin\left(ax\right)+C$, where $a=3$

$\left[\frac{1}{3}\sin\left(3x\right)\right]_{0}^{\pi }$
2

Evaluate the definite integral

$\frac{1}{3}\sin\left(3\pi \right)- \left(\frac{1}{3}\right)\sin\left(3\cdot 0\right)$

Final answer to the exercise

$\frac{1}{3}\sin\left(3\pi \right)- \left(\frac{1}{3}\right)\sin\left(3\cdot 0\right)$

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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Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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