How can this integral be solved? int[0,1] cos(2x + 5) dx

[lasvegas666]

 

[khansaheb]

View attachment 37813

If I were to solve this problem
I would start with substitution

u = 2*x +5

I would also convert dx and the "integration limits" accordingly.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[lasvegas666]

If I were to solve this problem
I would start with substitution

u = 2*x +5

I would also convert dx and the "integration limits" accordingly.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

Alright,
and du = 2.

What do we do after that?

 

[skeeter]

du = 2 dx

substitute and reset the limits of integration from x to u values

 

[lasvegas666]

du = 2 dx

substitute and reset the limits of integration from x to u values

What do we do after this to arrive at our final answer?

 

[mario99]

What do we do after this to arrive at our final answer?

Replace $dx$ with $\displaystyle \frac{1}{2} \ du$

 

[lasvegas666]

Replace $dx$ with $\displaystyle \frac{1}{2} \ du$

Okay, and then what do we do next?

 

[mario99]

Okay, and then what do we do next?

Integrate $\frac{1}{2}\cos u$

 

[lasvegas666]

Integrate $\frac{1}{2}\cos u$

Okey doke.

Are we getting closer to the final answer?

 

[lookagain]

Okey doke.

Are we getting closer to the final answer?

I would like to know that you have covered similar problems in a course and have notes on it. You have been
asking for little steps along the way very frequently instead of writing down in the thread much progress in
one post. As tutors/helpers, we are here to help reinforce concepts with what you are already supposed to have
learned, not teach you how to solve the problem, and especially not do it with you not being a participant by
not sharing your work in the posts.

 

[khansaheb]

Okey doke.

Are we getting closer to the final answer?

Are you in an instructional class?

Do you have a textbook to follow? You should!

What does the text-book say? Review the worked-out examples in the textbook.

 

[willbill]

I would change the $$dx$$ to $$d(2x + 5)$$

 

[khansaheb]

change the dx to d(2x+5)

That would be incorrect.

Evaluate: Integrate [0 to 1] cos(2x+5) dx

$\displaystyle \int_{0}^{1}cos(2x+5) dx$.....................substitute

u = (2x+5).....................&

du = 2 dx

Change Upper limit of integration.........1 $\displaystyle \to$ 7................and

Change Lower limit of integration.........0 $\displaystyle \to$ 5................thus

$\displaystyle \int_{0}^{1}cos(2x+5) dx$ ................. transforms to

$\displaystyle \int_{5}^{7}\frac{cos(u)}{2} du$

=(1/2) * [sin(7) - sin(5)]..............Now use your calculator to finish it

 

[mario99]

I would change the $$dx$$ to $$d(2x + 5)$$

You mean:

$\displaystyle dx = \frac{1}{2}d(2x + 5)$

Then

$\displaystyle \frac{1}{2}\int_{0}^{1} \cos(2x + 5) \ d(2x + 5) = \frac{1}{2}\sin(2x + 5)\bigg|_0^1$