JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

f(x)

be a continuous function such that the area bounded by the curve

y=f(x)

, the

x

-axis, and the lines

x=0

and

x=a

1+\frac{a^2}{2} \sin a.

Then,

View answer and explanation

Correct option: C

f(a)=a \sin a+\frac{1}{2} a^2 \cos a

Option C (

f(a)=a \sin a+\frac{1}{2} a^2 \cos a

) is correct because it is obtained by differentiating the given integral equation using the Fundamental Theorem of Calculus and the product rule.

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