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Calculate the definite integral of the function f(x)=2xf(x) = 2x from x=1x = 1 to x=3x = 3.

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Evaluate definite integrals using the chain ruleright chevron icon

Full solution

Q. Calculate the definite integral of the function f(x)=2xf(x) = 2x from x=1x = 1 to x=3x = 3.
  1. Write Integral: First, let's write down the integral we need to solve: ∫132x dx\int_{1}^{3} 2x \, dx.
  2. Find Antiderivative: Now, we find the antiderivative of 2x2x, which is x2x^2.
  3. Evaluate Integral: So, the integral becomes: [x2][x^2] from 11 to 33.
  4. Plug Upper Limit: We plug in the upper limit of the integral: 32=93^2 = 9.
  5. Plug Lower Limit: Then, we plug in the lower limit of the integral: 12=11^2 = 1.
  6. Subtract Results: Subtract the lower limit result from the upper limit result: 9−1=89 - 1 = 8.

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