Definite-Integration Question 515
Question: If $ \varphi (x)=\int_{1/x}^{\sqrt{x}}{\sin (t^{2}),dt,} $ then $ {\varphi }’(1)= $
Options:
A) $ \sin 1 $
B) $ 2\sin 1 $
C) $ \frac{3}{2}\sin 1 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \varphi ‘(x)=\sin x\frac{d}{dx}\sqrt{x}-\sin \frac{1}{x^{2}}\frac{d}{dx}( \frac{1}{x} ) $ $ =\sin x.\frac{1}{2\sqrt{x}}+\frac{1}{x^{2}}\sin \frac{1}{x^{2}} $
Þ $ \varphi ‘(1)=\frac{1}{2}\sin 1+\sin 1=\frac{3}{2}\sin 1 $ .
BETA
