Theorems on Integration

Q.

If $\int f\left(x\right)dx=F\left(x\right)$, then $\int f\left(5x\right)dx=\frac{F\left(5x\right)}{5}+C$

1. True

2. False

Q. For each positive integer $n$, let
$y_n=\frac{1}{n}\left\{\right(n+1\left)\right(n+2)......(n+n){\}}^{\frac{1}{n}}$

For $x\in R$ let $\left[x\right]$ be the greatest integer less than or equal to $x$. If $\underset{n\to \infty }{lim}{y}_n=L$, then the value of $\left[L\right]$ is

Q. For $\int f\left(x\right)dx=F\left(x\right)+C$, if $\int 4f(2x+3)dx=aF(2x+3)+C$, then the value of $a$ is

1. 2
2. 3
3. 4
4. 8