Students can download 12th Business Maths Chapter 2 Integral Calculus I Ex 2.3 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 2.3

Integrate the following with respect to x.

Question 1.

\(e^{x \log a}+e^{a \log a}-e^{n \log x}\)

Solution:

Question 2.

\(\frac{a^{x}-e^{x \log b}}{e^{x \log a} b^{x}}\)

Solution:

Question 3.

\(\left(e^{x}+1\right)^{2} e^{x}\)

Solution:

Question 4.

\(\frac{e^{3 x}-e^{-3 x}}{e^{x}}\)

Solution:

Question 5.

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

Solution:

Question 6.

\(\left[1-\frac{1}{x^{2}}\right] e^{\left(x+\frac{1}{x}\right)}\)

Solution:

Question 7.

\(\frac{1}{x(\log x)^{2}}\)

Solution:

Question 8.

If f'(x) = e^{x} and f(0) = 2, then find f(x).

Solution:

f'(x) = e^{x}

Integrating both sides of the equation,

∫ f'(x) dx = ∫ e^{x} dx

⇒ f(x) = e^{x} + c

given f(0) = 2

2 = e^{0} + c

⇒ c = 1

Thus f(x) = e^{x} + 1