Definite Integration Question 252
Question: If $ f(x)=\int _{x^{2}}^{x^{4}}{\sin \sqrt{t}dt,} $ then $ {f}’(x) $ equals
Options:
A) $ \sin x^{2}-\sin x $
B) $ 4x^{3}\sin x^{2}-2x\sin x $
C) $ x^{4}\sin x^{2}-x\sin x $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ f(x)=\int _{x^{2}}^{x^{4}}{\sin \sqrt{t}}dt $
$ f’(x)=\frac{d}{dx}(x^{4})(\sin \sqrt{x^{4}})-\frac{d}{dx}(x^{2})(\sin \sqrt{x^{2}}) $
$ =4x^{3}\sin x^{2}-2x\sin x $ .
BETA
