1. ## Integral Problem

Hello! I am a senior in high school who is taking AP Calculus. I'm stuck on this problem. I tried several methods to solve this, but couldn't match any of my answers with the choices. Any help would be wonderful. Thank you in advance!

If $\displaystyle \int^3_{0}f(x)dx=6$ and $\displaystyle \int^5_{3}f(x)dx=4$, then $\displaystyle \int^5_{0}(3+2f(x))dx=$

2. F(3) - F(0) = 6
F(5) - F(3) = 4

$\displaystyle \int_{0}^{5} f(x)dx = F(5) - F(0) = 10$

Now they're just playing games from here.

$\displaystyle \int_{0}^{5}(3+2f(x))dx = \int_{0}^{5}3dx + \int_{0}^{5}2f(x)dx = 3 \int_{0}^{5}dx + 2\int_{0}^{5}f(x)dx$

3. Hi derfleurer! Thank you so much for your help! And a quick response at that! I finally got an answer from the choices, which was 35. I understood everything you said. I'll be sure to remember this for future exams and problems!

4. Originally Posted by mamori
Hi derfleurer! Thank you so much for your help! And a quick response at that! I finally got an answer from the choices, which was 35. I understood everything you said. I'll be sure to remember this for future exams and problems!
Originally Posted by derfleurer
F(3) - F(0) = 6
F(5) - F(3) = 4

$\displaystyle \int_{0}^{5} f(x)dx = F(5) - F(0) = 10$

Now they're just playing games from here.

$\displaystyle \int_{0}^{5}(3+2f(x))dx = \int_{0}^{5}3dx + \int_{0}^{5}2f(x)dx = 3 \int_{0}^{5}dx + 2\int_{0}^{5}f(x)dx$
A thing I might add without the use of antiderivatives is

$\displaystyle \int_{0}^{3}f(x)dx + \int_{3}^{5}f(x)dx = \int_{0}^{5}f(x)dx$

5. Do you have any idea how slow I am at typing LaTeX? =p

6. Originally Posted by derfleurer
Do you have any idea how slow I am at typing LaTeX? =p
It gets better (besides a copy and paste works well). Did you notice that you can type the latex code and then highlight and then use the $\displaystyle \Sigma$ in the tool bar?

7. Do you have any idea how pitifully JavaScript handles under IE5.5?Shoot me. =p