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About Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience
Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

You are here: Experts > Teens > Homework/Study Tips > Calculus > High School level Calculus

Topic: Calculus

Expert: Abe Mantell
Date: 1/3/2004
Subject: High School level Calculus

Question
How would I go about solving this problem:

The problem gives me the solution of
y= The integral from 0 to x sin(tsquared)dt+xcubed+x+2

It also tells me that the differential equation is y(double prime)=2xcos(xsquared)+6x
and it tells me the inital conditions yprime(0)=1 and y(0)=2

How do I confirm this solution?
Thank You

Answer
Hello Molly,

Well, just take the first and second derivative of the
given solution, substitute them in to the DE and make
sure it works.

But how do you take the derivative of an integral you ask?

d/dx[Int(f(t),from t=a to x] = f(x)

So, the derivative of y is:
y' = sin(x^2) + 3x^2, now you can find y'' and check...

OK?

Abe

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