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int_(1)^(4)(3-|x-3|)dx

2424. ∫14(3−∣x−3∣)dx \int_{1}^{4}(3-|x-3|) d x

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Evaluate definite integrals using the chain ruleright chevron icon

Full solution

Q. 2424. ∫14(3−∣x−3∣)dx \int_{1}^{4}(3-|x-3|) d x
  1. Evaluate Integral: Evaluate the integral of the function 3−∣x−3∣3 - |x-3| from 11 to 44.
  2. Split at x=33: Split the integral at x=3x=3 and simplify the absolute value.
  3. Calculate First Integral: Calculate the first integral from 11 to 33.
  4. Calculate Second Integral: Calculate the second integral from 33 to 44.
  5. Add Results: Add the results of the two integrals.

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