The function g(x) is odd and continuous for all x. If int_(0)^(a)g(x)dx=3.5, what is int_(-a)^(a)g(x)dx?

Identify Odd Function: Since g(x) is an odd function, the integral of g(x) from -a to 0 is the negative of the integral from 0 to a. Calculate Integral from -a to 0: Calculate the integral of g(x) from -a to 0, which is -3.5 because the integral from 0 to a is 3.5. Find Integral from -a to a: Add the integral from -a to 0 and from 0 to a to find the integral from -a to a. So, -3.5 + 3.5 = 0.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The function
g(x) is odd and continuous for all
x. If
int_(0)^(a)g(x)dx=3.5, what is
int_(-a)^(a)g(x)dx?

The function $g(x)$ is odd and continuous for all $\mathrm{x}$ . If $\int_{0}^{a} g(x) d x=3.5$ , what is $\int_{-a}^{a} g(x) d x ?$

View step-by-step help

Home

Math Problems

Calculus

Find indefinite integrals using the substitution and by parts

Full solution

Q. The function

g(x)

is odd and continuous for all

\mathrm{x}

. If

\int_{0}^{a} g(x) d x=3.5

, what is

\int_{-a}^{a} g(x) d x ?

Identify Odd Function: Since $g(x)$ is an odd function, the integral of $g(x)$ from $-a$ to $0$ is the negative of the integral from $0$ to $a$ .
Calculate Integral from $-a$ to $0$ : Calculate the integral of $g(x)$ from $-a$ to $0$ , which is $-3.5$ because the integral from $0$ to $a$ is $3.5$ .
Find Integral from $-a$ to $a$ : Add the integral from $-a$ to $0$ and from $0$ to $a$ to find the integral from $-a$ to $a$ . So, $-3.5 + 3.5 = 0$ .