Check your IQ with this Integration

Calculus Level 2

$\large \begin{cases} y=0 \\ y = f(x) \\ x = c \\ x=d \end{cases}$

If the area bounded by above curves is independent of $d$ , $\forall\ d > c$ , then $f(x)$ is:

Note: $c$ is a constant.

Exponential Function Zero function Identity Function A non-zero constant function None of these Parabolic Function

1 solution

Arghyadeep Chatterjee
Oct 5, 2020

As $\displaystyle \int_{c}^{d}f(x)\,dx=0$ we have,

$\displaystyle \frac{\partial}{\partial d} \int_{c}^{d}f(x)\,dx=0$

Hence By Leibnitz Rule for Differentiating under the integral sign:-

$f(d) = 0,\,\, \forall \,d$ . Hence $f(x)$ is a zero function.