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Class 12 Maths Study Material

An Educational platform for Preparation and Practice Class 12. Kidsfront provide unique pattern of learning Maths with free online comprehensive study material in the form of QUESTION & ANSWER for each Chapter of Maths for Class 12. This study material help Class 12, Maths students in learning every aspect of Integrals. Students can understand Integrals concept easily and consolidate their learning by doing Online Practice Tests on Maths,Integrals chapter repeatedly till they excel in Class 12, Integrals. Free ONLINE PRACTICE TESTS on Class 12, Integrals comprise of Hundreds of Questions on Integrals, prepared by the highly professionals team. Every repeat test of Integrals will have new set of questions and help students to prepare themselves for exams by doing unlimited Online Test exercise on Integrals. Attempt ONLINE TEST on Class 12,Maths,Integrals in Academics section after completing this Integrals Question Answer Exercise.

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Integrals

If f(x) and g(x) are two real value functions such that∫ f(x)dx and∫ g(x)dx exist, then

a) ∫k f(x)dx = k∫ f(x)dx
b) ∫k f(x)dx - k∫ f(x)dx
c) ∫k f(x)dx + k∫ f(x)dx
d) All of these

✔Answer

Correct Answer Is : ∫k f(x)dx = k∫ f(x)dx

Solution Is :

If∫ f(x)dx = F(x), then∫ f (ax + b)dx =

a) 1/a F(ax + b) + c; a?0
b) 1/a F(ax + b) + c; a=0
c) A F(ax + b) + c; a?0
d) F(ax + b) + c; a?0

✔Answer

Correct Answer Is : 1/a F(ax + b) + c; a?0

Solution Is :

Evaluate: ∫(3x + 4)^3 dx

a) (3x + 4)^4
b) (3x + 4)^2
c) (3x + 4)^4/12
d) (3x + 4)^4/4

✔Answer

Correct Answer Is : (3x + 4)^4/12

Solution Is :

Evaluate: ∫cos^3 x.dx

a) 3sin x /4 + c
b) 3sin x /4 + 3sin 3x /4 + c
c) 3sin x /4 + 3sin 3x /12
d) 3sin x /4 + 3sin 3x /12 + c

✔Answer

Correct Answer Is : 3sin x /4 + 3sin 3x /12 + c

Solution Is :

True or false: if a and b are any non-zero real number,∫(e^(ax + b))dx=e^(ax + b)

a) TRUE
b) FALSE
c) Maybe
d) None of these

✔Answer

Correct Answer Is : FALSE

Solution Is :

Evaluate: ∫sin 7x.cos 3x.dx

a) (-cos 10x/20) - (cos4x/8) + c
b) (-cos 10x/20) + (cos4x/8) + c
c) (-cos 10x/20) - (cos4x/4) + c
d) (-cos 10x/2) - (cos4x/8) + c

✔Answer

Correct Answer Is : (-cos 10x/20) - (cos4x/8) + c

Solution Is :

Integrate the function f(x) = (1/ 1 + cos x) with respect to x.

a) Tan x + c
b) Tan x/2 + c
c) Cot x/2 + c
d) Cot x + c

✔Answer

Correct Answer Is : Tan x/2 + c

Solution Is :

Integrate the function f(x) = (tan x / sec x + tan x) with respect to x.

a) Sec x - tan x + x + c
b) Sec x + tan x + x + c
c) Sec x - tan x - x + c
d) Sec x - tan x + c

✔Answer

Correct Answer Is : Sec x - tan x + x + c

Solution Is :

What are the different methods of integration?

a) Integration by substitution
b) Some special integrals
c) Integrals of type ∫(1/ax^2 + bx + c)dx
d) All of these

✔Answer

Correct Answer Is : All of these

Solution Is :

In which method, we reduced the given function to standard form by changing variable x to t, using some suitable substitution x = ∅(t).

a) Integration by substitution
b) Some special integrals
c) Integrals of type ∫(1/ax^2 + bx + c)dx
d) All of these

✔Answer

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Class 12 Maths Study Material

Integrals

If f(x) and g(x) are two real value functions such that∫ f(x)dx and∫ g(x)dx exist, then

Correct Answer Is : ∫k f(x)dx = k∫ f(x)dx

Solution Is :

If∫ f(x)dx = F(x), then∫ f (ax + b)dx =

Correct Answer Is : 1/a F(ax + b) + c; a?0

Solution Is :

Evaluate: ∫(3x + 4)^3 dx

Correct Answer Is : (3x + 4)^4/12

Solution Is :

Evaluate: ∫cos^3 x.dx

Correct Answer Is : 3sin x /4 + 3sin 3x /12 + c

Solution Is :

True or false: if a and b are any non-zero real number,∫(e^(ax + b))dx=e^(ax + b)

Correct Answer Is : FALSE

Solution Is :

Evaluate: ∫sin 7x.cos 3x.dx

Correct Answer Is : (-cos 10x/20) - (cos4x/8) + c

Solution Is :

Integrate the function f(x) = (1/ 1 + cos x) with respect to x.

Correct Answer Is : Tan x/2 + c

Solution Is :

Integrate the function f(x) = (tan x / sec x + tan x) with respect to x.

Correct Answer Is : Sec x - tan x + x + c

Solution Is :

What are the different methods of integration?

Correct Answer Is : All of these

Solution Is :

In which method, we reduced the given function to standard form by changing variable x to t, using some suitable substitution x = ∅(t).

Correct Answer Is : Integration by substitution

Solution Is :

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