CBSE Class 12 (Science) Integrals — practice questions
82 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Science) Integrals in the app →The integral $\int x^3\, dx$ equals:To evaluate $\int x\cos x\, dx$, the best technique is:Compute ∫ 2x sin(x²) dx using substitution:The integral ∫ x^n dx (for n ≠ -1) equals:By the Fundamental Theorem of Calculus, ∫_0^2 (3x² + 2x) dx equals:The integral ∫_{-1}^{1} x³ dx equals:The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:The improper integral ∫_1^∞ (1/x²) dx evaluates to:By Walli's formula, ∫_0^(π/2) sin^4(x) dx equals:Integration is the process that undoes which operation?Any two antiderivatives of one function differ only by a:The arbitrary C added to every indefinite integral is named:Differentiating which expression produces 3x^2?A student integrates cos x. What should she write?Which result is right for the antiderivative of sin x?Find the function whose derivative is sec x tan x.What is obtained on integrating cosec x cot x?For x not zero, the antiderivative of 1/x is:Which expression equals the integral of tan x?The result of integrating sec x is:Pulling a constant k out: the integral of k f(x) dx equals:Integrate 4x^3 - 6x term by term.What is the integral of sqrt(x) over x > 0?Antidifferentiate 1/x^2 for x not zero.Work out the integral of e^(2x).If t = 3x is substituted, the integral of cos 3x becomes:Use t = x^2 on 2x e^(x^2) dx; the antiderivative is:Since 2x is the derivative of 1 + x^2, the integral of 2x/(1 + x^2) is:Put t = 1 + x^3 and find the integral of x^2 / (1 + x^3).Which is the antiderivative of (2x + 1)^3?Substituting t = 1 + cos x, the integral of sin x/(1 + cos x) is:Using tan^2 x = sec^2 x - 1, integrate tan^2 x:Using the half-angle identity, cos^2 x integrates to:Integrating sin^2 x via (1 - cos 2x)/2 gives:Put t = sin x: the integral of cos x / sin^2 x is:Expand (x + 1/x)^2 and integrate to get:1/(1 + x^2) is the derivative of which function?Name the antiderivative of 1/sqrt(1 - x^2).Given the form 1/(x^2 + a^2), integrate 1/(x^2 + 9).Evaluate: integral of dx / sqrt(4 - x^2).Integrate 1/(x^2 - 4) by the (1/2a) log formula.With a positive, 1/(a^2 - x^2) integrates to:Completing the square, integrate 1/(x^2 + 2x + 5):What is the integral of (2x + 3)/(x^2 + 3x + 7)?A ratio P(x)/Q(x) with deg P less than deg Q is called:To integrate P/Q when deg P exceeds deg Q, begin by:Resolve (x + 3)/((x - 1)(x + 2)): what multiplies 1/(x - 1)?Which sum of partial fractions equals 1/(x(x + 1))?Integrating the partial fractions of 1/(x(x + 1)) gives:Which setup decomposes 1/((x-1)^2 (x+2))?Choose the correct decomposition of 1/((x-1)(x^2+1)).Integration by parts says the integral of f g equals:Find the integral of x e^x by taking x as the first function.Parts on x cos x: what is its antiderivative?What do we get on integrating x sin x by parts?Integrating log x by parts, the usual choice is:Compute the antiderivative of log x for x > 0.Parts on ln x times x^2: which function should go first?Integrate tan^-1 x using 1 as the second function:Find the integral of x^2 e^x by repeating parts twice.For e^x [f(x) + f'(x)], the integral is:Integrate e^x (tan x + sec^2 x).Integrate e^x (1/x - 1/x^2) over x > 0.In a definite integral from a to b, the numbers a and b are the:Geometrically, the integral of f from a to b measures:If A(x) is the area function of continuous f, then A'(x) =Find the area under y = x^2 between x = 0 and x = 1.Integral of 3x^2 from x = 0 to x = 2 equals:What does the integral of sin x give between 0 and pi?Value of the integral from 0 to pi/2 of cos x:Compute the integral of dx/x from x = 1 to x = e.Evaluate e^x integrated from 0 up to 1.Integrate sec^2 x from 0 to pi/4.Find the integral of (2x + 1) from 1 to 3.Integral of 2x/(1 + x^2) over [0, 1] equals:Evaluate the integral over [0, 1] of x e^(x^2).The integral of any odd function over [-a, a] is:For even f, the integral over [-a, a] is twice the integral over:Integral of cos x over [-pi/2, pi/2]:Using the 2a property, the integral of sin x from 0 to 2*pi is:Find integral of sin x/(sin x + cos x) from 0 to pi/2.To turn f(x) into f(a + b - x) in a definite integral, substitute: