Question

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

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

Suppose f is an even function and ?-6^6 f(x) dx = 6.
a. Evaluate ?0^6 f(x) dx
b. Evaluate ?-6^6 xf(x) dx
a. Evaluate the definite integral.
?0^6 f(x) dx = ? (Simplify your answer.)
b. Evaluate the definite integral.
?-6^6 xf(x) dx = ? (Simplify your answer.)

Added by Patrick R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Harsha M

02/03/2022

Step 1

Since f is an even function, the integral from -a to a of f(x) dx is twice the integral from 0 to a of f(x) dx. So, ∫ from -a to a of f(x) dx = 2 * ∫ from 0 to a of f(x) dx = 2 * 6 = 12. Show more…

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