TS EAPCET (Engineering) Integral Calculus — practice questions
46 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) 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?$ 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 =