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

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

(ii) \(\int_{0}^{π/2}\) cos⁷x dx
Solution:
Here n = 7, which is odd

(iii) \(\int_{0}^{π/4}\) sin⁶ 2x dx
Solution:
put t = 2x
dt = 2 dx

(iv) \(\int_{0}^{π/6}\) sin⁵ 3x dx
Solution:
put t = 3x
dt = 3 dx

(v) \(\int_{0}^{π/2}\) sin² x cos⁴ x dx
Solution:
Here m = 2, which is even and n = 4, which is even

(vi) \(\int_{0}^{2π}\) sin⁷ \(\frac{x}{4}\) dx
Solution:

(vii) \(\int_{0}^{π/2}\) sin³ θ cos⁵ θ dθ
Solution:

Aliter Method

(viii) \(\int_{1}^{0}\) x² (1 – x)³ dx
Solution:
By applying reduction formula