1. ## Intergrals

Can someone please hlep me/ show me how to do this problem!! thannks
1. Let .
Find ????
and ???
Note: You should use the first part to do the second part!

2. Use the First Fundamental Theorem of Calculus to find the derivative of

2. Originally Posted by Kayla_N
Can someone please hlep me/ show me how to do this problem!! thannks
1. Let .
Find ????
and ???
Note: You should use the first part to do the second part!

2. Use the First Fundamental Theorem of Calculus to find the derivative of
properties of definite integrals

1. $\displaystyle \int_6^{15} f(x) \, dx = \int_6^9 f(x) \, dx + \int_9^{12} f(x) \, dx + \int_{12}^{15} f(x) \, dx$

solve for $\displaystyle \int_9^{12} f(x) \, dx$ ... you were given the values for all the other definite integrals.

$\displaystyle \int_{12}^9 7f(x) - 7 \, dx =$

$\displaystyle 7\int_{12}^9 f(x) - 1 \, dx = -7\int_9^{12} f(x) - 1 \, dx = -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx$

2. if $\displaystyle F(x) = \int_a^x f(t) dt$ , then $\displaystyle F'(x) = f(x)$

3. Originally Posted by skeeter
properties of definite integrals

1. $\displaystyle \int_6^{15} f(x) \, dx = \int_6^9 f(x) \, dx + \int_9^{12} f(x) \, dx + \int_{12}^{15} f(x) \, dx$

solve for $\displaystyle \int_9^{12} f(x) \, dx$ ... you were given the values for all the other definite integrals.

$\displaystyle \int_{12}^9 7f(x) - 7 \, dx =$

$\displaystyle 7\int_{12}^9 f(x) - 1 \, dx = -7\int_9^{12} f(x) - 1 \, dx = -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx$

2. if $\displaystyle F(x) = \int_a^x f(t) dt$ , then $\displaystyle F'(x) = f(x)$
So for the first part of number 1 i got = -3. so how do i plug this in to get the second part? I look at what you did for second part and still dont understand.. please explain more. Thanks

4. Originally Posted by Kayla_N
So for the first part of number 1 i got = -3. so how do i plug this in to get the second part? I look at what you did for second part and still dont understand.. please explain more. Thanks
It is expected that you can substitute $\displaystyle \int_{9}^{12} f(x) \, dx= -3$ into $\displaystyle -7\int_9^{12} f(x) \, dx + 7\int_9^{12} 1 \, dx$.

It is also expected that you can evaluate $\displaystyle \int_9^{12} 1 \, dx$.

Please say where you get stuck trying to do these two things.