Question

help please anyone good in calculus and please explain step by step it would be really great.

Answer 1

\[If F(x)=\int\limits_{0}^{x}\frac{ 1 }{ t^2+1 }dt --> then F'(x)=\]

Answer 2

the derivative of the integral is the integrand

Answer 3

\[F(x)=\int_a^xf(t)dt\to F'(x)=f(x)\]

Answer 4

there is really no "step" here
where you see a \(t\) in the expression \(\frac{1}{t^2+1}\) replace it by an \(x\)

Answer 5

so its \[-\frac{ x^2 }{ x^2+1 }\]

Answer 6

no

Answer 7

replace \(t\) by \(x\) in \(\frac{1}{t^2+1}\)
there is no minus sign
there is no \(x\) in the numerator

Answer 8

Fundamental Theorem of Calculus

Answer 9

but the derivative is not the same

Answer 10

not the same as what?

Answer 11

as the original

Answer 12

they are the same

Answer 13

\[F(x)=\int _0^x\sin(t)dt\]
\[F'(x)=\sin(x)\]

Answer 14

\[F(x)=\int_0^x e^{-\frac{t^2}{2}}dt\]
\[F'(x)=e^{-\frac{x^2}{2}}\]

Answer 15

ok i get now thank u all but can u check my answers for other problems because i think some of them are wrong