If f(x) = int_{-1}^{x} |t| , dt, then for any | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $f(x) = \int_{-1}^{x} |t| \, dt$. For $x \geq 0$, we can split the integral at $t=0$: $f(x) = \int_{-1}^{0} |t| \, dt + \int_{0}^{x} |t| \,

Vedclass · Accepted Answer

$\frac{1}{2}(1+x^2)$

Vedclass · Answer

(C) Given $f(x) = \int_{-1}^{x} |t| \, dt$. For $x \geq 0$, we can split the integral at $t=0$: $f(x) = \int_{-1}^{0} |t| \, dt + \int_{0}^{x} |t| \, dt$. Since $|t| = -t$ for $t $f(x) = \int_{-1}^{0} (-t) \, dt + \int_{0}^{x} t \, dt$. Evaluating the integrals: $f(x) = \left[ -\frac{t^2}{2} \right]_{-1}^{0} + \left[ \frac{t^2}{2} \right]_{0}^{x}$. $f(x) = \left( 0 - (-\frac{(-1)^2}{2}) \right) + \left( \frac{x^2}{2} - 0 \right)$. $f(x) = \frac{1}{2} + \frac{x^2}{2} = \frac{1}{2}(1+x^2)$.

If $f(x) = \int_{-1}^{x} |t| \, dt$, then for any $x \geq 0$, $f(x)$ is equal to

Similar Questions

At a certain place,the angle of dip is $60^{\circ}$ and the horizontal component of the earth's magnetic field $(B_H)$ is $0.8 \times 10^{-4} ~T$. The earth's overall magnetic field is

$A$ diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32V$,the efficiency of the engine is:

An image formed by a concave mirror of focal length $6 \ cm$ is $3$ times the size of the object. What is the distance of the object from the mirror in $cm$?

Which of the following is a non-reducing sugar?

Vedclass Test Series

Exam Paper Generator

Online Exam Module