UPCET / UPSEE Integral Calculus — practice questions
27 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice UPCET / UPSEE Integral Calculus in the app →Indefinite integral of xⁿ (n ≠ -1):∫ (1/x) dx =∫ e^x dx =∫ sin x dx =∫ cos x dx =Linearity of integration: ∫ [af(x) + bg(x)] dx =∫ tan x dx =Integration by substitution: ∫ 2x × e^(x²) dx = (let u = x²)∫ from 0 to π/2 sin x dx =Integration by parts formula:∫ x e^x dx (by parts: u = x, dv = e^x dx):∫ from 0 to 1 x² dx =∫ ln x dx (by parts: u = ln x, dv = dx):∫ from -a to a (odd function) dx =Fundamental theorem of calculus: ∫ from a to b f'(x) dx =∫ 1/(1 + x²) dx =∫ from 0 to π sin²x dx =∫ x sin x dx (integration by parts):∫ sec²x dx =Area under y = x² from x = 0 to x = 2:∫ from 0 to ∞ e^(-x) dx =∫ x ln x dx (integration by parts: u = ln x, dv = x dx):∫ from 1 to e (1/x) dx =Reduction formula example: ∫ sinⁿ x dx (for n ≥ 2) =∫ from 0 to 2 (x² - 2x) dx =For ∫ dx / sqrt(a² - x²), let x = a sin θ. Result:∫ from 0 to π/2 sin x cos x dx =