- #1
tropic9393
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Homework Statement
If F(x)=∫from 0 to g(x) of 1/(√(1+t^3)) dt and g(x)= ∫from 0 to cos(x) of 1+sin(t^2) dt, then find f'(pi/2)
Homework Equations
The Attempt at a Solution
Tried FTC parts 1 and 2
Hello tropic9393. Welcome to PF !tropic9393 said:Homework Statement
If F(x)=∫from 0 to g(x) of 1/(√(1+t^3)) dt and g(x)= ∫from 0 to cos(x) of 1+sin(t^2) dt, then find f'(pi/2)
Homework Equations
The Attempt at a Solution
Tried FTC parts 1 and 2
You are correct regarding the anti-derivative of sin(t2).tropic9393 said:I know I need to solve for g(x). I did the integral with respect to t of and got realized that sin(t^2) does not have an elementary integral, and I haven't learned how to do solve for that yet.
Then i tried applying FTC directly and but i thought that only applied to the derivative of an integral.
I have a major conceptual block, so i don't really have a lot of work to show
Not quite right. You forgot to use the chain rule.tropic9393 said:f'(x)=1/(√(1+g(x)^3)
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FTC integrate multiple functions is a mathematical concept in which multiple functions are combined and evaluated using the fundamental theorem of calculus. This allows for the calculation of a definite integral over a given interval.
FTC integrate multiple functions is important because it allows for the evaluation of complex integrals that cannot be solved using basic integration techniques. It also provides a more efficient method for solving integrals, saving time and effort in mathematical calculations.
FTC integrate multiple functions is commonly used in scientific research, particularly in fields such as physics, engineering, and economics. It is used to analyze and model various physical systems and phenomena, as well as to calculate important quantities such as work, energy, and probability.
The two parts of FTC integrate multiple functions are the first fundamental theorem of calculus, which states that the definite integral of a function can be evaluated by finding an antiderivative of the function, and the second fundamental theorem of calculus, which states that the derivative of an integral is equal to the original function.
While FTC integrate multiple functions is a powerful tool in mathematics and science, it does have some limitations. It cannot be used to solve all integrals, particularly those involving discontinuous or undefined functions. It also requires a good understanding of calculus and careful attention to the limits of integration.