Definite Integral

abilitiesz

New member
Joined
Oct 4, 2009
Messages
15
I asked a new question on my hw at the bottom.



helpxr.jpg


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

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

Hence, 39f(x)dx = 63 = 93f(t)dt\displaystyle Hence, \ \int_{3}^{9}f(x)dx \ = \ 63 \ = \ \int_{9}^{3}-f(t)dt

Now if 93f(t)dt = 63, then 93f(t)dt = 63\displaystyle Now \ if \ \int_{9}^{3}-f(t)dt \ = \ 63, \ then \ \int_{9}^{3}f(t)dt \ = \ -63
 
Ohh, I understand now. I was making it harder than necessary. Thank you for elaborating on the problem for me.
 
Top