68 free MCQs on Integrals, each with its own worked answer and explanation. Indefinite and definite integrals, areas under curves
Take the timed Integrals chapterwise test →68 practice questions on Integrals, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Integrals notes.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.
Q1.
Integration is the reverse of:
Q2.
Integral of xⁿ dx = (n not equal to -1)
Q7.
What does C represent in integration?
Q10.
Evaluate definite integral: integral from 0 to 1 of x dx
Q14.
Definite integral represents:
Q17.
Integral of √x dx =
Q18.
Integral of (3x² + 2x + 1) dx =
Q20.
The upper and lower limits in a definite integral are written:
Q21.
Integrate: (1+x)² dx
Q22.
Integrate: sin²x dx using identity
Q23.
Integrate: e<sup>3x</sup> dx
Q24.
Integral of 1/(x²+a²) dx =
Q26.
Integrate using substitution: integral of 2x(x²+1)⁵ dx
Q27.
Integrate by parts: integral of x eˣ dx
Q28.
Integral of 1/√(1-x²) dx =
Q30.
Integral of tan x dx =
Q32.
Integrate: (3x² + 2x) / (x³ + x²) dx
Q34.
Integral of sec x tan x dx =
Q35.
Integrate: integral of x ln x dx (by parts)
Q36.
Using partial fractions, integrate: 1/((x-1)(x+1)) dx
Q38.
Integral of cosec²x dx =
Q39.
The area between y = x and y = x² from x = 0 to x = 1 is:
Q40.
Integrate: (1 + tan²x) dx
Q41.
Evaluate: integral of x²/(1+x³) dx
Q42.
Integral from 0 to π/2 of sin<sup>n</sup>(x)/(sin<sup>n</sup>(x)+cos<sup>n</sup>(x)) dx =
Q43.
Evaluate integral of √(1+x²) dx.
Q44.
Integral of (x+1)/((x+2)(x+3)) dx using partial fractions:
Q46.
Reduction formula for integral of sin<sup>n</sup>(x) dx when n is positive integer involves:
Q47.
Integral of 1/(a + b cosx) dx uses the substitution:
Q48.
The Beta function B(m,n) = integral from 0 to 1 of x<sup>m-1</sup>(1-x)<sup>n-1</sup> dx is related to Gamma by:
Q49.
Evaluate: integral from 0 to ∞ of e<sup>-x²</sup> dx.
Q50.
Using shell method, volume of solid of revolution of y=x² (0 to 1) around y-axis:
Q51.
integral of sin<sup>3</sup>(x) dx =
Q53.
Integral of e<sup>x</sup> cos(x) dx =
Q55.
Integral from a to b of f(x) dx = - integral from b to a of f(x) dx. This is because:
Q56.
Wallis product: (π/2) = product of [2n/(2n-1)] × [2n/(2n+1)] for n=1,2,3,...
Q57.
Evaluate: integral of (sin 2x)/(1+sin²x) dx.
Q58.
Second Mean Value Theorem for integrals: integral from a to b of f(x)g(x) dx =
Q59.
The volume of solid formed by rotating y=√x (from 0 to 4) around x-axis:
Q61.
The value of the definite integral of sin²x from 0 to π/2 is:
Q62.
The value of the definite integral of x/(1 + x²) from 0 to 1 is:
Q63.
The value of the definite integral of x·sinx from 0 to π is:
Q64.
The value of the definite integral of 1/(1 + tanx) from 0 to π/2 is:
Q65.
The value of the definite integral of lnx from 1 to e is:
Q66.
The value of the definite integral of the greatest integer function [x] from 0 to 2 is:
Q67.
The value of the definite integral of x³·e<sup>x²</sup> from −1 to 1 is:
Q68.
The indefinite integral of 1/(x² + 4) is:
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