Start learning →

MP Board Class 12 (MPBSE) Integral Calculus — practice questions

Explore 22 free Integral Calculus questions in MP Board Class 12 (MPBSE) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Integral Calculus with Quill →

Integral Calculus questions and exercises with answers

Showing questions 1–22 of 22.

The integral $\int x^3\, dx$ equals:Read the answer and worked solution →To evaluate $\int x\cos x\, dx$, the best technique is:Read the answer and worked solution →Complete the relationship between the two calculiRead the answer and worked solution →True or false: the constant of integrationRead the answer and worked solution →Differentiation or integration?Read the answer and worked solution →Tap every property of indefinite integrals the chapter givesRead the answer and worked solution →Properties in useRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: check an indefinite integralRead the answer and worked solution →Flip and pair: term with meaningRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →True or false: reading the notationRead the answer and worked solution →Definite or indefinite?Read the answer and worked solution →Reading the definitions backRead the answer and worked solution →Complete the linearity rulesRead the answer and worked solution →Which process is being described?Read the answer and worked solution →True or false: what the constant meansRead the answer and worked solution →Checking an integralRead the answer and worked solution →Tap every true statement about integrationRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →

Worked practice questions

The integral $\int x^3\, dx$ equals:

  1. $3x^2 + C$, the derivative of $x^3$ instead on chart
  2. $x^3 + C$, missing the power-up rule on chart entirely
  3. $x^4/4 + C$, by power rule for integration of $x^n$
  4. $4x^4 + C$, the wrong scaling factor on the chart here
Show answer and solution

Correct answer: C. $x^4/4 + C$, by power rule for integration of $x^n$

$\int x^n\, dx = x^{n+1}/(n+1) + C$ gives $x^4/4 + C$.

Open this question →

To evaluate $\int x\cos x\, dx$, the best technique is:

  1. Direct substitution $u = \cos x$ on the chart at one step
  2. Partial fractions, since the integrand is a rational function
  3. Trigonometric identity simplification on the school chart
  4. Integration by parts with $u = x$, $dv = \cos x\, dx$
Show answer and solution

Correct answer: D. Integration by parts with $u = x$, $dv = \cos x\, dx$

Integration by parts: $u = x$, $dv = \cos x\, dx$ gives $du = dx$, $v = \sin x$ result $x\sin x + \cos x + C$.

Open this question →

Complete the relationship between the two calculi

Read exercise and reference answers
Missing parts
  1. Answer
    derivative
    Choices
    1. derivative
    2. integral
    3. limit
  2. Answer
    function
    Choices
    1. function
    2. constant
    3. slope
  3. Answer
    inverse
    Choices
    1. inverse
    2. same
    3. square
Complete the statement
In differential calculus you are given a function and find its {0}. In integral calculus you are given the differential and must find the {1}. So integration is the {2} of differentiation.
Integration undoes differentiation. Source: syllabus Maths, Ch 7 Integrals.

Open this exercise →

How to practise

  1. Choose a Integral Calculus question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Vectors & 3D GeometryBinomial TheoremGeometryPermutations and CombinationsProbability & StatisticsSequencesSequences and SeriesThree Dimensional Geometry