Saturday

December 20, 2014

December 20, 2014

Posted by **Sean** on Sunday, March 16, 2008 at 7:47am.

(x^2+100)y'=23

When y(10sqrt(3))=0

Also, I have to find the indefite integral

of

xsqrt(19x-7), using integration tables in teh back of the book "Calculus of a Single Variable, 8th Edition." Tables are in appendix B

I used the formula

[2/[b(2n-3)]]*([u^n]*(a+bu)^[3/2]-na[integral of [u^(n-1)sqrt[a+bu]]]

I've used

a=-7

b=19

u=x

du=xd

But it doesn't seem to work.

- Calculus III -
**Count Iblis**, Sunday, March 16, 2008 at 10:37amUnless you really have to finish a problem in a hurry, never use integration tables or other tools for problem solving. Only use them to very the solution when you are done.

(x^2+100)y'=23 ---->

dy/dx = 23/[x^2 + 100] ----->

y = Integral of dy =

Integral of 23 dx/[x^2 + 100], looks like an arctan to me.

Integral of x sqrt(19x-7)dx ?

Write the integral in terms of functins you do know the inegral of. Rewrite the factor of x as follows:

x = 1/19 (19 x) =

1/19 (19 x - 7 + 7) =

1/19 (19 x - 7) + 7/19

I think you'll now see the answer. These sorts of tricks cannot be learned by just looking in integral tables.

- Calculus III -
**Sean**, Sunday, March 16, 2008 at 11:12amI got the first one, thanks for that.

But on the second one, are you saying that x=(1/19)*(19x-7)+(7/19)?

If so, would I just multiply the entire thing out, or what?

**Answer this Question**

**Related Questions**

Calculus - Integrals - Here's my first question: (FIrst part courtesy of Count ...

Calculus - Use integration by parts to evaluate the integral xsqrt(2x+6)dx.

Calculus - Hello, I'm having trouble with this exercise. Can you help me? ...

Calculus - Given a function f(x)=sqrt(100-x^2) Evaluate the integral xsqrt(100-x...

calculus - LEt f and g be continous functions with the following properties i. ...

calculus - LEt f and g be continous functions with the following properties i. ...

integration by parts - s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1...

Calculus II - Integrate using integration by parts (integral) (5-x) e^3x u = 5-x...

calc - evaluate the integral: y lny dy i know it's integration by parts but i ...

Calculus - How do you do this question. f(x) = (5x-1)/(2-3x), find f^(-1)(x). ...