AP EAPCET (Engineering) Integrals — practice questions
90 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Integrals in the app →Find $\displaystyle\int x^4\,dx$.Find $\displaystyle\int in x\,dx$.Evaluate $\displaystyle\int_{0}^{\pi/2} in x\,dx$.Find $\displaystyle\int 2x \cos(x^2)\,dx$.Find $\displaystyle\int x e^x\,dx$.Find $\displaystyle\int \dfrac{1}{(x-1)(x+1)}\,dx$.∫ x dx equals:∫ cos x dx equals:∫ sin x dx equals:∫ eˣ dx equals:∫ dx/x for x > 0 equals:∫ sec² x dx equals:∫ (3x² - 4x + 5) dx equals:Definite integral ∫₀¹ x² dx equals:∫ sec x tan x dx equals:By substitution u = x², ∫ 2x sin(x²) dx equals:∫ dx/(1 + x²) equals:∫ dx/√(1 - x²) equals:∫ x eˣ dx (using integration by parts):∫₀^(π/2) sin x dx equals:∫ ln x dx (by parts):∫₀¹ x e^(x²) dx equals:∫ dx/(x ln x) equals:∫ (x² + 1)/(x² - 1) dx equals:∫ sin³ x dx (using sin³ x = sin x (1 - cos² x)):∫ dx/√(x² + a²) equals:∫ dx/(x² + 4) equals:∫₀^(π) sin² x dx equals:∫₋ₐ^a x³ dx equals (for any a):∫ cosec² x dx equals:By partial fractions, ∫ dx/(x(x+1)) equals:∫₀^(2π) cos x dx equals:Area under y = x² from x = 0 to x = 2:∫ x sin x dx (by parts):∫ dx/(a² - x²) (for |x| < a):∫₀^(π/2) sin x cos 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):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.Integrating log x by parts, the usual choice is:Integrate tan^-1 x using 1 as the second function: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: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.