Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.6 Textbook Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.6

Question 1.

Evaluate the following

(i) \(\int_{0}^{π/2}\) sin^{10}x dx

Solution:

Here n = 10, which is even

(ii) \(\int_{0}^{π/2}\) cos^{7}x dx

Solution:

Here n = 7, which is odd

(iii) \(\int_{0}^{π/4}\) sin^{6} 2x dx

Solution:

put t = 2x

dt = 2 dx

(iv) \(\int_{0}^{π/6}\) sin^{5} 3x dx

Solution:

put t = 3x

dt = 3 dx

(v) \(\int_{0}^{π/2}\) sin^{2} x cos^{4} x dx

Solution:

Here m = 2, which is even and n = 4, which is even

(vi) \(\int_{0}^{2π}\) sin^{7} \(\frac{x}{4}\) dx

Solution:

(vii) \(\int_{0}^{π/2}\) sin^{3} θ cos^{5} θ dθ

Solution:

Aliter Method

(viii) \(\int_{1}^{0}\) x² (1 – x)³ dx

Solution:

By applying reduction formula