Daily Practice Problems
Class 12 Maths
Integrals Question 1:

Find the anti-derivative of (ax + b)2

Question 2:

Find the value of ∫ √tan x/(sin x * cos x) dx

Question 3:

Solve: ʃ [(x3 + 5x2 - 4)/x2] dx

Question 4:

Find: ʃ (4x + 1)/√(2x2 + x - 3) dx

Question 5:

If (d/dx) f(x) is g(x), then the anti derivative of g(x) is

(a) f(x)

(b) f’(x)

(c) g’(x)

(d) None of the above

Question 6:

Find: ʃ (2x - 3)/{(x2 - 1)(2x + 3)} dx

Question 7:

If ∫ 2x dx = f(x) + C, then f(x) is

(a) 2x

(b) 2x loge2

(c) 2x / loge2

(d) 2x+1/(x + 1)

Question 8:

Find: ʃ12 [(5x2)/(x2 + 4x + 3)]dx

Question 9:

If ∫ sec²(7 – 4x) dx = a * tan (7 – 4x) + C, then value of a is

(a) -4

(b) -1/4

(c) 3

(d) 7

Question 10:

Find: ʃ0π/2 [cos5 x/(sin5 x + cos5 x)] dx

Question 11:

Integrate: (e2x – e-2x)/(e2x + e-2x)

Question 12:

Find: ʃ dx/(x2 + 2x + 2)

Question 13:

Find: ʃ14 [|x - 1| + |x - 2| + |x - 3|] dx

Question 14:

ʃ dx/√(4 - 9x2) = (1/3) * sin-1(ax) + C, then the value of a is

(a) 2

(b) 4

(c) 3/2

(d) 2/3

Question 15:

Find: ʃ0π [(x * tan x)/(sec x + tan x)] dx

Question 16:

If a is such that 0a x dx ≤ a + 4, then

(a) 0 ≤ a ≤ 4

(b) -2 ≤ a ≤ 0

(c) a ≤ -2 or a ≤ 4

(d) -2 ≤ a ≤ 4

Question 17:

-11 |1 - x| dx is equal to _____.

Question 18:

Find: ʃ (x + 1)√(1 - x – x2) dx

Question 19:

ʃ [(10 x9 + 10x loge 10)/(x10 + 10x)] dx equals to ______.

Question 20:

Evaluate: -π/3π/3 x5 * sin6 x dx

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