Take Class 12 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Let's use trig substitution to solve a problem.
∫ x² / (√ 1 - x²) dx
Let x = sin θ. dx = cos θ dθ. Substituting
∫ sin² θ cos θ / √ 1 - sin² θ dθ
= ∫ sin² θ cos θ / √ cos² θ dθ
,= ∫ sin² θ cos θ / cos θ dθ. ( cos θ cancels out )
= ∫ sin² θ dθ. { sin² θ =1/2 ( 1 - cos 2θ ) }
= 1/2 ∫ (1 - cos 2θ ) dθ
= 1/2 ∫ dθ - ∫ cos 2θ dθ
= 1/2 ( θ - 1/2 sin 2θ ) + C
= 1/2 [ arc sin x - 1/2 ( 2 sin θ cos θ ) ] +C
= 1/2 arc sin x - 1/2 x ( √1 - x² ) + C
Find Class 12 Tuition near you
Learn from Best Tutors on UrbanPro.
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near you24 Answers
10 Answers
14 Answers
The best tutors for Class 12 Tuition Classes are on UrbanPro
The best Tutors for Class 12 Tuition Classes are on UrbanPro
0
