Class 12 ISC Maths integration Important Questions Part-1

Integration is called the inverse process of differentiation. Instead of differentiating a function, we are given the function’s derivative and asked to find its primitive, i.e., the original function. Such a process is called integration or anti-differentiation. If the function’s derivative is known to us, is it possible to obtain the function. The answer to this question is yes. Integration ( or antiderivative of a function) makes it possible to obtain the original function.

Class 12 ISC Maths integration Important Questions Part-1

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Q1 ∫ e log e √x⁄xdx

Q2 9log3xdx

Q3 ∫ e3log x (x4)dx

Q4 ∫√ (1-sin 2x)dx

Q5 ∫ sin x + cos x⁄√ (1 + sin 2x)

Q6 ∫ cos x - cos 2x⁄1 - cos x

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Q7 ∫ (ex loga + e a logx - ea loga)dx

Q8 ∫ 2x⁄(2x + 1)2dx

Q9 ∫ (3x + 1)√ 2x - 1dx

Q10 ∫ x + 2⁄√ 3x + 1 dx

Q11 ∫ sin 7x sin x dx

Q12 ∫ (sin6x + cos6x)dx

Q13 ∫ 1 + cos 4x⁄cot x - tan xdx

Q14 ∫ 6x2 + 1⁄(4x3 + 2x - 5)3dx

Q15 ∫ 1 + cotx⁄x + log sin x dx

Q16 ∫ dx⁄x cos2 (1 + log x)

Q17 ∫ e-x cosec2 (2e-x + 5)dx

Q18 ∫ ex(1+x)⁄cos2(xex)dx

Q19 ∫ cosec x⁄log (tan x⁄2) dx

Q20 ∫ sin 2x⁄(a + b cos x)2dx

Q21 ∫ cot x log sin x dx

Q22 ∫ sec x log | sec x + tan x| dx

Q23 ∫ cos5x⁄sin x

Q24 ∫ cos3x e log sin xdx

Q25 ∫ cosec6 x dx

Q26 ∫ tan 8 x sec 4 x dx

Q27 ∫ dx⁄√ sin3 x sin (x + ∝) dx

Q28 ∫ sin x - x cos x⁄x (x + sin x) dx

Q29 ∫ dx⁄√x + ∛x

Q30 ∫ (x4 - x)1/4⁄x5 dx

Q31 If f’(x) = a sinx + b cos x, f’(0) = 4, f(0) = 4, f(0) =3 and f(π/2)=5, find f(x).

Q32 Find the anti derivatives of the following functions:(x+1)(x+logx)⁄2x

Q33 Find the anti derivatives of the following functions:3(cos-1x)2⁄√ 1-x2

Q34 Find all the primitives of the following functions:x-2⁄2x2-8x 5 dx

Q35 Find all the primitives of the following functions:cosec2x⁄2 + 3 cot x dx

Q36 Find all the primitives of the following functions:x -1 ⁄x (x - log x)

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Q1 ∫ ^{e ^{log e √x}}⁄_xdx

Q2 9^log₃xdx

Q3 ∫ e^{3log x (x⁴)}dx

Q5 ∫ ^{sin x + cos x}⁄_{√

(1 + sin 2x)}

Q6 ∫ ^{cos x - cos 2x}⁄_{1 - cos x}

Q7 ∫ (e^{x loga} + e ^{a logx} - e^{a loga})dx

Q8 ∫ ^2x⁄_{(2x + 1)²}dx

Q10 ∫ ^{x + 2}⁄_{√

3x + 1} dx

Q12 ∫ (sin⁶x + cos⁶x)dx

Q13 ∫ ^{1 + cos 4x}⁄_{cot x - tan x}dx

Q14 ∫ ^{6x² + 1}⁄_{(4x³ + 2x - 5)³}dx

Q15 ∫ ^{1 + cotx}⁄_{x + log sin x} dx

Q16 ∫ ^dx⁄_{x cos² (1 + log x)}

Q17 ∫ e^-x cosec² (2e^-x + 5)dx

Q18 ∫ ^{e^x(1+x)}⁄_cos²(xe^x)dx

Q19 ∫ ^{cosec x}⁄_{log (tan ^x⁄₂)} dx

Q20 ∫ ^{sin 2x}⁄_{(a + b cos x)²}dx

Q23 ∫ ^cos⁵x⁄_{sin x}

Q24 ∫ cos³x e ^{log sin x}dx

Q25 ∫ cosec⁶ x dx

Q26 ∫ tan ⁸ x sec ⁴ x dx

Q27 ∫ ^dx⁄_{√

sin³ x sin (x + ∝)} dx

Q28 ∫ ^{sin x - x cos x}⁄_{x (x + sin x)} dx

Q29 ∫ ^dx⁄_{√x + ∛x}

Q30 ∫ ^{(x⁴ - x)^1/4}⁄_x⁵ dx

Q32 Find the anti derivatives of the following functions:^{(x+1)(x+logx)}⁄_2x

Q33 Find the anti derivatives of the following functions:^{3(cos^-1x)²}⁄_{√

1-x²}

Q34 Find all the primitives of the following functions:^x-2⁄_{2x²-8x
5} dx

Q35 Find all the primitives of the following functions:^cosec²x⁄_{2 + 3
cot
x} dx

Q36 Find all the primitives of the following functions:^{x -1}⁄_{x (x - log x)}