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Numerade Educator

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Problem 49 Easy Difficulty

If $ \displaystyle \int^9_0 f(x) \, dx = 37 $ and $ \displaystyle \int^9_0 g(x) \, dx = 16 $,
find $$ \int^9_0 \bigl[ 2f(x) + 3g(x) \bigr] \, dx $$

Answer

122

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Video Transcript

given that we know the integral from 0 to 9 is 37 0 to 9 of G of X is 16 then we want to evaluate this whole expression down here. Basically, you can always add to integral separately. So let's put a plus between these and then the other thing is we want to go ahead and multiply this by a factor of two, which we could just multiply out front, the integral of ffx and same thing with the integral on the right side. Here, let me just move this over and let's go ahead and put a three as a factor there, since that is multiplied by three in front of the integral of G of X. So basically two times all of this is the same thing as just two times 37. So to evaluate this, it's just going to be two times 37 waas three times. All of this is the same thing as three times 16. And when we simplify these two down that wind up giving us a total value of 122. Therefore, the Senate girl here combination of both with the extra factors there evaluates to 122