Fundamental Theorem of Calculus

Find the derivatives of the following functions $F\left(x\right)={\int }_{2/x}^{x^2}\frac{dt}{t}$.

Suppose $f$ and $g$ are integrable on $\left[a, b\right],$ then $f+g$ is integrable on _______

Find the area of the region bounded by x2=4y and y=2, y=4 and the Y-axis in the first quadrant.

Using integration, find the area of the region enclosed between the circles x2+y2=1 and (x-1)2+y2=1

If $f\left(x\right)=a$, then $\int f\left(x\right)dx=ax+C$, represents

If $f\left(x\right)=2x$, then $\int f\left(x\right)dx=x^2+C$, represents

$f\left(x\right)=\int 3x dx$, represents a family of curves

If $\int \frac{2\cos x-\sin x+\lambda }{\cos x+\sin x-2}dx=A\ln |\cos x+\sin x-2|+Bx+C$ , then the value of $A+B+\left|\lambda \right|$ is

Cotyledons are also called-

If $u=-f^{\prime \prime }\left(\mathrm{\theta }\right)\sin \mathrm{\theta }+f^{\prime }\left(\mathrm{\theta }\right)\cos \mathrm{\theta }$ and $v=f^{\prime \prime }\left(\mathrm{\theta }\right)\cos \mathrm{\theta }+f^{\prime }\left(\mathrm{\theta }\right)\sin \mathrm{\theta }$, then $\int f{\left[{\left(\frac{du}{d\mathrm{\theta }}\right)}^2+{\left(\frac{dv}{d\mathrm{\theta }}\right)}^2\right]}^{\frac{1}{2} }d\mathrm{\theta }$ is equal to