Question

Suppose f is an even function and $int_{-7}^{7} f(x) dx = 6$. a. Evaluate $int_{0}^{7} f(x) dx$ b. Evaluate $int_{-7}^{7} xf(x) dx$ a. Evaluate the definite integral. $int_{0}^{7} f(x) dx = square$ (Simplify your answer.) b. Evaluate the definite integral. $int_{-7}^{7} xf(x) dx = square$ (Simplify your answer.)

          Suppose f is an even function and $int_{-7}^{7} f(x) dx = 6$.
a. Evaluate $int_{0}^{7} f(x) dx$
b. Evaluate $int_{-7}^{7} xf(x) dx$
a. Evaluate the definite integral.
$int_{0}^{7} f(x) dx = square$ (Simplify your answer.)
b. Evaluate the definite integral.
$int_{-7}^{7} xf(x) dx = square$ (Simplify your answer.)

Suppose f is an even function and int-7^7 f(x) dx = 6.
a. Evaluate int0^7 f(x) dx
b. Evaluate int-7^7 xf(x) dx
a. Evaluate the definite integral.
int0^7 f(x) dx = square (Simplify your answer.)
b. Evaluate the definite integral.
int-7^7 xf(x) dx = square (Simplify your answer.)

Added by Beth W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sandip Ranjan

04/24/2022

Step 1

Since $f$ is even, we know that $\int_{-a}^{a} f(x) dx = 2 \int_{0}^{a} f(x) dx$. Therefore, $\int_{0}^{7} f(x) dx = 2 \times 6 = 12$. ** Show more…

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Suppose f is an even function and ∫ f(x) dx = 6. a. Evaluate ∫ f(x) dx b. Evaluate ∫ xf(x) dx a. Evaluate the definite integral. ∫ f(x) dx = (Simplify your answer.) b. Evaluate the definite integral. ∫ xf(x) dx = (Simplify your answer.)