Integration questions (1 Viewer)

[miasa]

Simple question but unfortunately, I don't know how to do it.
Find the indefinite integral of : dx(3x-2)^-1
Indefinite integral 6(e^2x)^-1
Find the area enclosed by the curve y=6x-x^2 and the x axis

 

[tashe]

Haven't done maths in more than 3 months and I've forgotten a lot of things.

Look at the attached picture.

Question 1:

line 2: You want a 3 on the numerator. This is because if you differentiate the denominator, you would end up with 3. You want the top to be the derivative of the denominator. Hence I added a 3 on the numerator. However, I changed the question. To fix that, I added 1/3 as well.
line 3: Normal integration.


Question 2:
line 2: I changed it to index form because that would make things easier.
line 3: To differentiate exponentials, you need to divide by the derivative of the power.


Question 3:
Step 1: Draw a quick sketch (or alternatively, equate to 0) to find the x-intercepts. The two intercepts will be your limits.
Step 2: Notice how it's concave down (as seen from your graph or the -x^2). This would mean we need to put a - in front of the integral.
Step 3: -INTEGRATE (6x-x^2) dx

Sorry that it's too wordy/going over the basics. It's been a while since I have done maths or explained maths.
Continue posting if you still don't get it.

 

[normalanus]

1) 1/3*log(3x-2)+c
2) -3e^-2x +c
3) Area= 36

General Mathematics represent