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JEE Main Definite Integration: related Mathematics practice

The practice bank below covers broader Mathematics topics; a dedicated Definite Integration lesson is not available yet.

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Mathematics questions and exercises with answers

Showing questions 1–3 of 3.

Match the integral to its resultRead the answer and worked solution →Order the steps to integrate ∫ x·eˣ dx by partsRead the answer and worked solution →Evaluate the definite integralRead the answer and worked solution →

Worked practice questions

Match the integral to its result

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Matching pairs
  1. Left
    ∫ x^n dx (n ≠ −1)
    Right
    x^(n+1)/(n+1) + C
  2. Left
    ∫ 1/x dx
    Right
    ln|x| + C
  3. Left
    ∫ e^x dx
    Right
    e^x + C

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Order the steps to integrate ∫ x·eˣ dx by parts

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Steps
  1. Identify u = x and dv = eˣ dx (using ILATE)
  2. Compute du = dx and v = eˣ
  3. Apply ∫u dv = uv − ∫v du
  4. Substitute: x·eˣ − ∫eˣ dx
  5. Evaluate the remaining integral: x·eˣ − eˣ + C

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Evaluate the definite integral

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Missing parts
  1. Answer
    −cos x
    Choices
    1. −cos x
    2. cos x
    3. sin x
  2. Answer
    −cos π
    Choices
    1. −cos π
    2. cos π
    3. sin π
  3. Answer
    −cos 0
    Choices
    1. −cos 0
    2. cos 0
    3. sin 0
  4. Answer
    2
    Choices
    1. 2
    2. 0
    3. π
Complete the statement
∫₀^π sin x dx = [{0}]₀^π = {1} − {2} = {3}

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