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) \(\int_{0}^{π/2}\) sin10x dx
Solution:
Here n = 10, which is even
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 1

Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6

(ii) \(\int_{0}^{π/2}\) cos7x dx
Solution:
Here n = 7, which is odd
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 2

Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6

(iii) \(\int_{0}^{π/4}\) sin6 2x dx
Solution:
put t = 2x
dt = 2 dx
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 3

(iv) \(\int_{0}^{π/6}\) sin5 3x dx
Solution:
put t = 3x
dt = 3 dx
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 4

Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6

(v) \(\int_{0}^{π/2}\) sin2 x cos4 x dx
Solution:
Here m = 2, which is even and n = 4, which is even
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 5

(vi) \(\int_{0}^{2π}\) sin7 \(\frac{x}{4}\) dx
Solution:
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 6

Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6

(vii) \(\int_{0}^{π/2}\) sin3 θ cos5 θ dθ
Solution:
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 7
Aliter Method
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 8

(viii) \(\int_{1}^{0}\) x² (1 – x)³ dx
Solution:
By applying reduction formula
Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6 9

Samacheer Kalvi 12th Maths Guide Chapter 9 Applications of Integration Ex 9.6