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NCERT Questions for Class 12 Maths Chapter 7 – Integrals
For students of Class 12, Integrals is one of the core concepts in calculus, through which we will be able to find the areas under curves, calculate volumes, and solve other real-life problems. The concept of integration is, therefore, very important in Math and related fields if one is to perform well. Here are some important questions and answers that will add weight to your knowledge and skills on integrals. These important NCERT questions were developed by specialists in accordance with the latest syllabus.
Important Questions with Solutions of Class 12 Maths Chapter 7 – Integrals
1) Evaluate:
Ans –
2) Evaluate:
Ans – We know cos2x + sin2x = 1
3) Evaluate:
Ans – Let u = x + 1, du = dx
⇒ u – 1 = x
Substitute the value of u we will get,
4) Evaluate:
Ans – Let u = log(sec x + tan x)
5) Evaluate:
Ans – We can write the expression as:
6) Evaluate:
Ans – Substitute
Resubstitute the value of u in the equation
7) Evaluate:
Ans – The expression can be modified as
We know the trigonometric formula 2 cos A cos B = cos(A + B) + cos(A – B)
Applying this in the equation we get,
We know the trigonometric formula cos 2θ = 2cos2θ – 1
Applying this in the equation we get,
8) Evaluate:
Ans – We can simplify the expression as,
Substitute u = x – (1/2) ⟺ du = dv
Substitute u = √5/3v ⟺ du = dv
Resubstitute v = 2/√5u and u = x – (1/2)
9) Evaluate:
Ans – We can write the given integral as
After simplifying we get,
10) Evaluate:
Ans – Divide and multiply the fraction by sin(x – α).
Substitute u = cos x ⟺ du = -sin x dx and v = sin x ⟺ dv = cos x dx in the above equation.
