Students can download 12th Business Maths Chapter 2 Integral Calculus I Ex 2.4 Questions and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

## Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.4

Integrate the following with respect to x.

Question 1.

2 cos x – 3 sin x + 4 sec^{2} x – 5 cosec^{2} x

Solution:

= ∫(2 cos x -3 sin x + 4 sec² x – 5 cosec² x) dx

= ∫2 cos x dx – ∫3 sin x dx + ∫4 sec² x dx – 5 ∫cosec²x dx

= 2(sin x) -3(-cos x) + 4 tan x – 5 (-cot x) + c

= 2 sin x + 3 cos x + 4 tan x + 5 cot x + c

Question 2.

∫ sin^{3} x dx

Solution:

We know that, sin 3x = 3 sin x – 4 sin^{3} x

Question 3.

\(\frac{\cos 2 x+2 \sin ^{2} x}{\cos ^{2} x}\)

Solution:

Question 4.

\(\frac{1}{\sin ^{2} x \cos ^{2} x}\)

[Hint: sin^{2} x + cos^{2} x = 1]

Solution:

Question 5.

\(\sqrt{1-\sin 2} x\)

Solution: