Integral problem

**abcocoa** · January 7th 2007, 10:57 AM

I'm reviewing for math finals, and have run into a road block wit hthis problem:

If the integral of f(x)dx from a to b equals a+2b, then the integral of
(f(x) +5)dx from a to b equals what?

I know how to do integrals when given the actual function, but have no idea how that +5 is going to affect the result in general. Can someone give me an idea of how to solve this kind of problem? The answer is supposed be 7b-5a. Thanks!

**ThePerfectHacker** · January 7th 2007, 11:00 AM

Originally Posted by abcocoa

I'm reviewing for math finals, and have run into a road block wit hthis problem:

If the integral of f(x)dx from a to b equals a+2b, then the integral of
(f(x) +5)dx from a to b equals what?

I know how to do integrals when given the actual function, but have no idea how that +5 is going to affect the result in general. Can someone give me an idea of how to solve this kind of problem? The answer is supposed be 7b-5a. Thanks!

$\int_a^b f(x)+ 5 dx=\int_a^b f(x)dx+\int_1^b 5dx=a+2b+5(b-a)$

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