# A few integral questions i need help with!

1. Jun 8, 2005

### laker_gurl3

Evaluate the integrals:

(integral sign) {2x^3 - 7x^2 + 3x^1/2 -x}dx
So when i evaluated this integral, i got:

1/2X^4 - 7/3X^3 + 2*(3)^1/2 / 3 X^3/2 - X^2 +C

oookay, so that looks a bit confusing...so if you don't understand that, can someone post me the answer to this question?

My other question is:

Solve the following differential equation:

dy/dx = sinx-sec^2x

For this question, i got
-cosx-tanx+C
is that one correct?

Lastly, i would like to know if i got this answer right..
A pebble is tossed 6m/s down a cliff 72m high. how long will it take to hit the ground?
my final answer was 3.27 seconds..

any help would work you guys! thanks so much!

2. Jun 8, 2005

### VietDao29

Uhm, number 1 is wrong.
2 and 3 look fine to me.
Viet Dao,

3. Jun 8, 2005

### laker_gurl3

so what's the right answer for number 1..? i dont know how else to do it..

4. Jun 8, 2005

### Nylex

Look back at your answer and see. Some of the terms are wrong. Edit: the first two terms are ok.

Last edited: Jun 8, 2005
5. Jun 9, 2005

### laker_gurl3

okay, so how do i find the integral of square root 3X? cuz i have a feeling that's the wrong term in my answer..i dont know how to go about finding it..

6. Jun 9, 2005

### Nylex

The way you had it written wasn't clear, it looked like it was $3x^\frac{1}{2}$. If you did mean $(3x)^\frac{1}{2}$ then that term is right too.The last one is still wrong though.

7. Jun 9, 2005

### laker_gurl3

ooh okay, is the last term - (1/2)X^2

8. Jun 9, 2005

Yes, it is.

9. Jun 9, 2005

### laker_gurl3

okay thanks alot! another question i had was

Solve the following differential equation:
dy/dx = sec(y)sin(x) y= (pi/2) when x = pi

i changed the sec(y) to 1/(cos(y)) then multiplied to the dy side so this is what it looks like now

sec(y) dy = sin(x) dx + C

then i antideriv of the both side

sin(y) dy = -cos(x) + C

subbed in the pi/2 and pi then i got:

C = 0

Is that a good enough answer or do i have to write it in a different form?
thanks a bunch!

10. Jun 9, 2005

### laker_gurl3

bump... thanks a lot you guys

11. Jun 9, 2005

### siddharth

How did you get that equation.
Shouldn't it be
cos(y)dy=sin(x)dx?

What's the 'dy' term doing after you find the anti-derivative on both sides?