Definite Integral - 2 questions i need help with

[Benji195]

Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]

1) Rewrite Q into the form of

[MATH] \int_{B}^{A}\frac{MS+C}{S^{2}+K^{2}}[/MATH]
Where a, b, c, k, m are constants

2) Hence, Evaluate Q

 

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[Deleted member 4993]

Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]

1) Rewrite Q into the form of

[MATH] \int_{B}^{A}\frac{MS+C}{S^{2}+K^{2}}[/MATH]
Where a, b, c, k, m are constants

2) Hence, Evaluate Q

I have several questions about your post:

1. What is the difference between "X" and "x"? You have both in: Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]
   
2. We are supposed to integrate relative to which variable "dx" or "dX"
   
   If you had shown some work, answers to these questions would have been apparent - and we would start "helpful" helping!

 

[Benji195]

I need help finding the top section ms+c. Will it be 2(x-3)+4?

Q = [MATH]\int_{3}^{5}\frac{need help}{(x-3)^{2}+4} [/MATH]dx

Would then 2nd answer be which i just need to evaluate?

Q = [MATH]\int_{0}^{2}\frac{t^{2}+4}{t^{2}+4^{2}} [/MATH]dx

 

[Benji195]

I have several questions about your post:

1. What is the difference between "X" and "x"? You have both in: Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]
   
2. We are supposed to integrate relative to which variable "dx" or "dX"
   
   If you had shown some work, answers to these questions would have been apparent - and we would start "helpful" helping!

Sorry should be

Define Q =[MATH] \int_{5}^{3}\frac{2(x+1)}{x^{2}-6x+13}dx [/MATH]

 

[Deleted member 4993]

I need help finding the top section ms+c. Will it be 2(x-3)+4?

Q = [MATH]\int_{3}^{5}\frac{need help}{(x-3)^{2}+4} [/MATH]dx

Would then 2nd answer be which i just need to evaluate?

Q = [MATH]\int_{0}^{2}\frac{t^{2}+4}{t^{2}+4^{2}} [/MATH]dx

According to given hint in OP,

S = ?

K = ?

 

[Benji195]

Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]

1) Rewrite Q into the form of

[MATH] \int_{B}^{A}\frac{MS+C}{S^{2}+K^{2}}[/MATH]
Where a, b, c, k, m are constants

2) Hence, Evaluate Q

According to given hint in OP,

S = ([MATH]x-3[/MATH])

K = [MATH]4^{2}[/MATH]
?

 

[Benji195]

Here is an example answer to a similar question for
[MATH]\int_{3}^{4}\frac{4x}{x^{2}-6+10}dx[/MATH]

. I need to answer the original question in the same way

 

[Steven G]

I need help finding the top section ms+c. Will it be 2(x-3)+4?

Q = [MATH]\int_{3}^{5}\frac{need help}{(x-3)^{2}+4} [/MATH]dx

Would then 2nd answer be which i just need to evaluate?

Q = [MATH]\int_{0}^{2}\frac{t^{2}+4}{t^{2}+4^{2}} [/MATH]dx

Maybe distribute the 2 in 2(X+1) = 2X+ 2
By the way you do realize that in mathematics that X and x are NOT the same variable?

 

[Deleted member 4993]

Define Q =[MATH] \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} [/MATH]

1) Rewrite Q into the form of

[MATH] \int_{B}^{A}\frac{MS+C}{S^{2}+K^{2}}[/MATH]
Where a, b, c, k, m are constants

2) Hence, Evaluate Q

using

S = x - 3 \(\displaystyle \to \) dS = dx and when x = 5 \(\displaystyle \to \) S = 2 and when x = 3 \(\displaystyle \to \) S = 0

we get M(x-3) + C = 2x + 2

Mx = 2x \(\displaystyle \to \) M = 2, and

-3M + C = 2 \(\displaystyle \to \) C = 8

So now we have,

Q = \(\displaystyle \int_{5}^{3}\frac{2(X+1)}{X^{2}-6x+13} dx \) = \(\displaystyle \int_{2}^{0}\frac{2S + 8}{S^{2} + 2^2} dS\)

=\(\displaystyle \int_{2}^{0}\frac{2S}{S^{2} + 2^2} dS\) + \(\displaystyle \int_{2}^{0}\frac{8}{S^{2} + 2^2} dS\)

Continue.....