Evaluate: int_{-a}^a f(x) dx - int_0^a f(-x) | vedclass

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

Question

(C) We know that the property of definite integrals states: $\int_{-a}^a f(x) dx = \int_{-a}^0 f(x) dx + \int_0^a f(x) dx$. By substituting $x = -t$ i

Vedclass · Accepted Answer

$\int_0^a f(a-x) dx$

Vedclass · Answer

(C) We know that the property of definite integrals states: $\int_{-a}^a f(x) dx = \int_{-a}^0 f(x) dx + \int_0^a f(x) dx$. By substituting $x = -t$ in the first integral $\int_{-a}^0 f(x) dx$,we get $\int_a^0 f(-t) (-dt) = \int_0^a f(-t) dt = \int_0^a f(-x) dx$. Therefore,$\int_{-a}^a f(x) dx = \int_0^a f(-x) dx + \int_0^a f(x) dx$. Substituting this into the given expression: $(\int_0^a f(-x) dx + \int_0^a f(x) dx) - \int_0^a f(-x) dx = \int_0^a f(x) dx$. Using the property $\int_0^a f(x) dx = \int_0^a f(a-x) dx$,the result is $\int_0^a f(a-x) dx$.

Evaluate: $\int_{-a}^a f(x) dx - \int_0^a f(-x) dx$

Similar Questions

If $\int_{-1}^{4} f(x) dx = 4$ and $\int_{2}^{4} (3 - f(x)) dx = 7$,then the value of $\int_{2}^{-1} f(x) dx$ is

Find the value of $\int_{0}^{1} \frac{\log (1+x)}{1+x^{2}} d x$.

Let $(a, b)$ be the point of intersection of the curve $x^2=2y$ and the straight line $y-2x-6=0$ in the second quadrant. Then the integral $I=\int_a^b \frac{9x^2}{1+5^x} dx$ is equal to:

By using the properties of definite integrals,evaluate the integral $\int_{2}^{8}|x-5| d x$.

The value of $\int_{0}^{\pi /2} \frac{2^{\sin x}}{2^{\sin x} + 2^{\cos x}} dx$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module