Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.4 Textbook Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.4

Question 1.

Evaluate the following

\(\int_{0}^{1}\) x³e^{-2x} dx

Solution:

Bernoulli’s formula,

∫uv dx = uv_{1} – u^{1}v_{2} + u^{2}v_{3} – u^{3}v_{4} + ….

Question 2.

\(\int_{0}^{1}\) \(\frac{sin(3tan^{-1}x)tan^{-1}x dx}{1+x^2}\)

Solution:

Question 3.

\(\int_{0}^{1/√2}\) \(\frac{e^{sin^{-1}x}sin^{-1}x}{\sqrt{1-x^2}}\) dx

Solution:

Question 4.

\(\int_{0}^{\pi / 2}\) x² cos 2x dx

Solution: