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JEE Main Integrals — practice questions

Explore 61 free Integrals questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integrals questions and exercises with answers

Showing questions 1–30 of 61.

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 →Differential calculus grew from the problem of defining:Read the answer and worked solution →Integral calculus grew from the problem of calculating:Read the answer and worked solution →A function whose derivative is the given function is its:Read the answer and worked solution →The formula giving all the anti derivatives is the:Read the answer and worked solution →Knowing the velocity of an object at each instant, one can find its:Read the answer and worked solution →How many anti derivatives does a function have?Read the answer and worked solution →The constant C added to an anti derivative is called:Read the answer and worked solution →The constant C in an indefinite integral is also called the constant of:Read the answer and worked solution →Two functions with the same derivative differ by a:Read the answer and worked solution →Varying C in an anti derivative traces out a:Read the answer and worked solution →The two forms of the integral are the definite and the:Read the answer and worked solution →The result linking indefinite and definite integrals is the:Read the answer and worked solution →The definite integral is useful in science and:Read the answer and worked solution →In an indefinite integral, x is called the variable of:Read the answer and worked solution →Integration and differentiation are related as:Read the answer and worked solution →An anti derivative is also known as a:Read the answer and worked solution →Adding a different constant to an anti derivative gives:Read the answer and worked solution →The family of anti derivatives of a function is written with:Read the answer and worked solution →The problem of finding a function from its derivative leads to the:Read the answer and worked solution →The problem of finding an area under a graph leads to the:Read the answer and worked solution →A function whose derivative is zero throughout an interval is:Read the answer and worked solution →True or false on integralsRead the answer and worked solution →Quick picks on calculusRead the answer and worked solution →Match each term to its meaningRead the answer and worked solution →Differential or integralRead the answer and worked solution →Definite or indefiniteRead the answer and worked solution →Recover a function from its derivativeRead 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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