### Video Transcript

The function π is odd, continuous
on the closed interval negative one to seven, and satisfies the definite integral
between one and seven of π of π₯ with respect to π₯ equals negative 17. Determine the definite integral
between negative one and seven of π of π₯ with respect to π₯.

Weβre firstly told that the
function π is odd. So we recall the following property
for integrating odd functions. The definite integral between
negative π and π of π of π₯ with respect to π₯ is equal to zero. Weβre also told that the definite
integral between one and seven of π of π₯ with respect to π₯ is equal to negative
17. So we split the integral up. And we see that the integral that
weβre looking for between negative one and seven of π of π₯ with respect to π₯ is
equal to the definite integral between negative one and one of π of π₯ plus the
definite integral between one and seven of π of π₯.

Now, the function π is odd. So by the first property, we see
that the definite integral between negative one and one of π of π₯ with respect to
π₯ must be equal to zero. Then, we simply take the definite
integral between one and seven of π of π₯ from the question. Itβs negative 17. This means the definite integral
weβre looking for is equal to zero plus negative 17 which is negative 17.