Definite Integral

[abilitiesz]

I asked a new question on my hw at the bottom.

I am unsure on how to start, but what i got was:

-(x^2/2), then i tried plugging in the 63, but my answer came out wrong.

Any help is appreciated, thank you.

 

[BigGlenntheHeavy]

\(\displaystyle Hint: \ c\int_ {a}^{b}f(x)dx \ = \ -c\int_ {b}^{a}f(t)dt\)

 

[abilitiesz]

Using your hint that you gave me, so do i do f(b) - f(a) , then times it by -63 which is the c that is outside? I'm still somewhat confused.

 

[BigGlenntheHeavy]

\(\displaystyle c \ \int_{a}^{b}f(x)dx \ = \ -c \ \int_{b}^{a}f(t)dt\)

\(\displaystyle Now, \ to \ keep \ it \ simple, \ let \ c \ =1, \ then \ \int_{a}^{b}f(x)dx \ = \ \int_{b}^{a}-f(t)dt\)

\(\displaystyle Hence, \ \int_{3}^{9}f(x)dx \ = \ 63 \ = \ \int_{9}^{3}-f(t)dt\)

\(\displaystyle Now \ if \ \int_{9}^{3}-f(t)dt \ = \ 63, \ then \ \int_{9}^{3}f(t)dt \ = \ -63\)

 

[abilitiesz]

Ohh, I understand now. I was making it harder than necessary. Thank you for elaborating on the problem for me.