TS EAMCET Integral Calculus — practice questions
102 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAMCET 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 =Applying the power rule, x^5 is integrated to which function?If d/dx F(x) = cos x, which expression can F(x) be?What does integrating the exponential function e^x return?Which function has derivative sec^2 x, up to a constant?For x > 0, integrating 1/x givesAn antiderivative family of sin x isWhich family is obtained from cosec^2 x dx?Integrating 1/sqrt(1 - x^2) over |x| < 1 yieldsWhat is the antiderivative of 1/(1 + x^2) valid for all real x?Up to a constant, which function differentiates to sec x tan x?Find F(x) if F'(x) = 3x^2 + 4x^3 and the constant is arbitrary.How many antiderivatives does the function f(x) = 2x have?Integrating x^(-2) on the nonzero reals givesThe constant function 5 is integrated over x; the result isFor a > 0 and a not equal to 1, the integral of a^x dx isUsing the substitution t = x^2, the integral of 2x e^(x^2) dx becomesRewriting tan x as sin x/cos x and integrating givesSubstituting t = sin x in (cos x/sin x) dx leads to the familyThe standard result for integrating sec x involves which expression?Multiplying cosec x by (cosec x - cot x)/(cosec x - cot x) before integrating leads toSubstituting t = 2x + 1 integrates (2x + 1)^3 dx toLetting t = 2x, the integral of e^(2x) dx isLetting t = x^2 + 1 for x/(x^2 + 1) dx givesLetting t = ln x for (ln x)/x dx with x > 0 givesFor x > a > 0, 1/(x^2 - a^2) has which antiderivative?For |x| < a, the standard integral of 1/(a^2 - x^2) isPutting x = a tan t converts dx/(x^2 + a^2) into the familyFor a > 0, which antiderivative corresponds to dx/sqrt(a^2 - x^2)?With a = 3 in the standard arctangent form, 1/(x^2 + 9) integrates toFor x > 2, the rational function 1/((x - 1)(x - 2)) has antiderivativeThe partial fraction form of 1/((x + 1)^2 (x - 3)) isA rational function P(x)/Q(x) is called proper whenTaking x as the first function, x e^x is integrated toTaking ln x as the first function and 1 as the second givesTaking ln x as u and x dx as dv, the integral of x ln x ise^x (sin x + cos x) has the form e^x (f + f'); its integral isWith f = 1/x and x > 0, e^x (f + f') integrates toApplying parts twice to x^2 e^x givesIntegration by parts with u = x turns x sin x intoBy the LIATE rule, which function is best chosen as u in the integral of x e^x dx?Who introduced the notation for the indefinite integral in 1675?The integral symbol is adapted from the long letter s standing for which Latin word?Over the interval [0, pi], the integral of sin x equalsOver [0, 2], integrate 3x^2; the value isOver [1, e], the definite integral of 1/x isx^3 is integrated over [-2, 2]; the value isThe integral of e^x over [0, 1] equalsOdd integrand sin^3 x on the symmetric interval [-pi/2, pi/2] givesThe definite integral of sin x/(sin x + cos x) dx from 0 to pi/2 equalsIf the integral of f(x) dx from 1 to 4 is 7, the integral from 4 to 1 isEven integrand x^4 on [-1, 1] gives a value ofOver [0, pi], sin^2 x integrates toThe second fundamental theorem of integral calculus states that the integral of f from a to b equalsBy the first fundamental theorem, d/dx of the integral of t^2 dt from 0 to x equalsWith t = x^2, the integral of x e^(x^2) on [0, 1] givesIn which century did Leibniz and Newton independently discover the fundamental theorem of calculus?