Students can download 12th Business Maths Chapter 2 Integral Calculus I Ex 2.2 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 2.2

Integrate the following with respect to x.

Question 1.

\(\int\left(\sqrt{2 x}-\frac{1}{\sqrt{2 x}}\right)^{2}\)

Solution:

Question 2.

\(\frac{x^{4}-x^{2}+2}{x-1}\)

Solution:

Question 3.

\(\frac{x^{3}}{x+2}\)

Solution:

Question 4.

\(\frac{x^{3}+3 x^{2}-7 x+11}{x+5}\)

Solution:

We have to find the quotient by division

Question 5.

\(\frac{3 x+2}{(x-2)(x-3)}\)

Solution:

We use the partial fraction method to split the given function into two fractions and then integrate.

Question 6.

\(\frac{4 x^{2}+2 x+6}{(x+1)^{2}(x-3)}\)

Solution:

By partial fractions,

Question 7.

\(\frac{3 x^{2}-2 x+5}{(x-1)\left(x^{2}+5\right)}\)

Solution:

Question 8.

If f'(x) = \(\frac{1}{x}\) and f(1) = \(\frac{\pi}{4}\), then find f(x)

Solution: