# Thread: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation please!!!

1. ## Help with leaving integratio in the form a+bsqrt3 and simultaneous equation please!!!

1.Find the values of p and q which satisfy the following simultaneous equations
∫from2to1(px^2 + q) dx = 9
∫from2to1 (qx + p) dx = 6

2a) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

b) Hence evaluate
∫from3to0 (4sqrtx + 3)^2 dx

Giving your answer in the form a + bsqrt3 where a and b are integers.

Thanks!

2. ## Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

Originally Posted by shan
1.Find the values of p and q which satisfy the following simultaneous equations
∫from2to1(px^2 + q) dx = 9
∫from2to1 (qx + p) dx = 6

2a) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

b) Hence evaluate
∫from3to0 (4sqrtx + 3)^2 dx

Giving your answer in the form a + bsqrt3 where a and b are integers.
Are you asking for someone else to do your work for you?

3. ## Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

I have come across 2 questions that I am really struggling to answer and I would like to know how they are done?

4. ## Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

Originally Posted by shan
I have come across 2 questions that I am really struggling to answer and I would like to know how they are done?
If you are saying that you do not know how to evaluate $\int_1^2 {(qx + p)dx}$, then you need more instruction than we can give you.

5. ## Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

This was posted in the "algebra" forum. Perhaps shan has never taken a Calculus class and stumbled onto this problem by accident!

6. ## Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

Originally Posted by shan
1.Find the values of p and q which satisfy the following simultaneous equations
∫from2to1(px^2 + q) dx = 9
∫from2to1 (qx + p) dx = 6
If you have taken Calculus then you should know that the first equation is (p/3)x^3+ qx= 9 and the second (q/3)x^3+ px= 6.
Multiplying the first equation by q and the second by p, you have (pq/3)x^3+ q^2x= 9q and (pq/3)x^3+ p^3x= 6p. Subtracting (p^2- q^2)x= 6p- 9q.

2) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

b) Hence evaluate
∫from3to0 (4sqrtx + 3)^2 dx[tex]

Giving your answer in the form a + bsqrt3 where a and b are integers.

Thanks!
sqrt(x) is the same as x^(1/2) so you are being asked to integrate 16x+ 24x^(1/2)+ 9 with respect to x. Again, the integral of x^n is (1/(n+1))x^(n+1). The integral of 16x= 16x^1 is (1/2)x^2= 8x^2 and the integral of 24x^(1/2) is 24(2/3)x^(3/2)= 16x^(3/2). The integral of 9= 9x^0 is 9x.