The value of int_{-1}^{1} (sqrt{1 + x + x^2} | vedclass

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

Question

(A) Let $f(x) = \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}$.We check if the function is even or odd by evaluating $f(-x)$:$f(-x) = \sqrt{1 + (-x) + (-x)^

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let $f(x) = \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}$.We check if the function is even or odd by evaluating $f(-x)$:$f(-x) = \sqrt{1 + (-x) + (-x)^2} - \sqrt{1 - (-x) + (-x)^2}$$f(-x) = \sqrt{1 - x + x^2} - \sqrt{1 + x + x^2}$$f(-x) = -(\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) = -f(x)$.Since $f(-x) = -f(x)$,the function $f(x)$ is an odd function.For an odd function,the property of definite integrals states that $\int_{-a}^{a} f(x) \, dx = 0$.Therefore,$\int_{-1}^{1} (\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) \, dx = 0$.

The value of $\int_{-1}^{1} (\sqrt{1 + x + x^2} - \sqrt{1 - x + x^2}) \, dx$ is

Similar Questions

Which one of the following is mainly responsible for the depletion of the ozone layer?

An air-cored coil has a self-inductance of $0.1 \ H$. $A$ soft iron core of relative permeability $1000$ is introduced,and the number of turns is reduced to $\left(\frac{1}{10}\right)^{\text{th}}$. The value of the new self-inductance is:

Ammonia can be dried by

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

The angle between the lines $x \cos \alpha_1 + y \sin \alpha_1 = p_1$ and $x \cos \alpha_2 + y \sin \alpha_2 = p_2$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module