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vovangra [49]
2 years ago
12

Solve the attachment...​

Mathematics
1 answer:
hichkok12 [17]2 years ago
8 0

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 }}

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