Home > Calculus > Integrals of Exponential Functions

Let #F(x)=int_(0)^xsqrt(1+t^2)dt# how to find #F'(x)#?

Answer 1

Aurora Alvarado

As #f(x) = sqrt(1+x^2)# is continuous for any #x in RR#, based on the fundamental theorem of calculus:

#d/dx (int_0^x sqrt(1+t^2)dt) = sqrt(1+x^2)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isabella Ackerman

To find ( F'(x) ) for the function ( F(x) = \int_0^x \sqrt{1 + t^2} , dt ), you can apply the Fundamental Theorem of Calculus, which states that if ( F(x) ) is the integral of ( f(x) ), then ( F'(x) = f(x) ).

So, in this case, ( F'(x) = \sqrt{1 + x^2} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.