GUJCET Integral Calculus — practice questions
48 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice GUJCET Integral Calculus in the app →A fair coin is tossed twice. How many outcomes are there in the sample space?A fair six-sided die is rolled once. What is the probability of getting an even number?Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice iA card is drawn at random from a standard $52$-card deck. What is the probability that the card is either a ki$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:General solution of cos θ = 0:The arithmetic mean of n values x1, x2, ..., xn is:Median of an odd-length sorted data set is:Probability of a certain event:Probability of rolling a 6 on a fair die:For independent events A and B, P(A and B) equals: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 =