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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 37 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 37 Maths Textbook Solution.

Answers (1)

Answer:

\frac{\cos ^{5} x}{5}-\frac{\cos ^{7} x}{7}+C

Given:

\int \sin ^{3} x \cos ^{4} x d x

Hint:

To solve the statement we will convert cos into sin and use some formula of 2sin(A+B) and 2sin(A-B)

Solution:

\int \sin ^{3} x\cos ^{4}x d x

put

\int \sin x \cdot \sin ^{2} x \cdot \cos ^{4} x d x

p u t \: \cos x=t, \sin x d x=d t

  \int \sin x\left(1-\cos ^{2} x\right) \cdot \cos ^{4} x d x\left[\sin ^{2} x=1-\cos ^{2} x\right]

   \int\left(1-t^{2}\right) t^{4} d t

      \int t^{4}-t^{6} d t

    \int t^{4} d t-\int t^{6} d t

 \int \frac{t^{5}}{5}-\frac{t^{7}}{7}

   t=\cos x

\frac{\cos ^{5} x}{5}-\frac{\cos ^{7} x}{7}+C

 

Posted by

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