JEE Main Integrals — practice questions
62 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main 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 inverse process of:$\displaystyle\int x^n\,dx$ (for $n\neq -1$) equals:$\displaystyle\int \cos x\,dx$ equals:$\displaystyle\int \frac{1}{x}\,dx$ equals:$\displaystyle\int e^x\,dx$ equals:The arbitrary constant $C$ added in an indefinite integral is called the:$\displaystyle\int x^2\,dx$ equals:$\displaystyle\int in x\,dx$ equals:The value of $\displaystyle\int_0^1 x\,dx$ is:$\displaystyle\int ec^2 x\,dx$ equals:The value of $\displaystyle\int_0^{\pi/2} \cos x\,dx$ is:$\displaystyle\int 2x\,dx$ equals:The technique used to integrate a product of two functions is called:The integral $\int x^3\, dx$ equals:The definite integral $\int_0^1 x\, dx$ equals:To evaluate $\int x\cos x\, dx$, the best technique is:If $f$ is an odd function, $\int_{-a}^a f(x)\, dx$ equals:Compute ∫ 2x sin(x²) dx using substitution:In integration by parts (∫u dv = uv − ∫v du), the LIATE rule helps choose 'u'. For ∫x ln(x) dx, the correct chThe integral ∫ x^n dx (for n ≠ -1) equals:By the Fundamental Theorem of Calculus, ∫_0^2 (3x² + 2x) dx equals:The integral ∫_{-1}^{1} x³ dx equals:The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:The improper integral ∫_1^∞ (1/x²) dx evaluates to:By Walli's formula, ∫_0^(π/2) sin^4(x) dx equals:When the integrand has NO simple anti-derivative (like e^{-x²}), the most common numerical method is: