Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 2 Integral Calculus I Ex 2.2 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 2 Integral Calculus I Ex 2.2

Question 1.

Integrate the following with respect to x.

[\(\sqrt { 2x}\) – \(\frac { 1 }{\sqrt { 2x}}\)]²

Solution:

Question 2.

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

Solution:

Question 3.

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

Solution:

Question 4.

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

Solution:

Question 5.

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

Solution:

By partial fraction

Question 6.

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

Solution:

By partial fraction

⇒ 4x² + 2x + 6 = A (x + 1)² + B (x – 3) (x + 1) + c (x – 3)

Put x = 3

4(9) + 2(3) + 6 = A(4)²

36 + 6 + 6 = 16A ⇒ A = \(\frac { 48 }{16}\)

A = 3

Put x = -1

4(1) + 2(-1) + 6 = C(-4)

4 – 2 + 6 = -4C ⇒ -4c = 8

C = -2

Put x = 0

6 = A(1) + B(-3) + C(-3)

6 = 3(1) – 3B + (-2) (-3)

6 = 3 – 3B + 6 ⇒ 3B = 3

B = 1

Question 7.

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

Solution:

Question 8.

Given f'(x) = \(\frac { 1 }{x}\) and f (1) = \(\frac { 1 }{π}\), then find f(x)

Solution:

f'(x) = \(\frac { 1 }{x}\)

f(x) = ∫f'(x) dx = ∫\(\frac { 1 }{x}\) dx

f(x) = log|x| + c

f(1) = π/4 ⇒ log|1| + c = π/4.

⇒ 0 + c = π/4

∴ c = π/4

∴ Required f (x) = log |x| + π/4