Question

Solve the attachment...​

Answer 1

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

$\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx$

Here 5 is a constant so it can come out . So that,

$\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx$

Now we can write √x as ,

$\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx$

Simplify ,

$\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx$

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

$\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg)$

On simplifying we will get ,

$\longrightarrow \underline{\underline{ I = 2 }}$

Answer 2

Answer:

Step-by-step explanation:

=  $\int\limits^1_0 {5x\sqrt{x} } \, dx$

=  $\int\limits^1_0 {5xx^{1/2} } \, dx$

= $\int\limits^1_0 {5x^{3/2} } \, dx$

= 5 $\int\limits^1_0 {x^{3/2} } \, dx$

= 5*$\frac{2}{5}$*$x^{5/2}$  |$\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left$

= 5*$\frac{2}{5}$*$1^{5/2}$

= 2