UPCET / UPSEE Integrals — practice questions
36 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice UPCET / UPSEE 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: