Question

Bangla - নিক পয়েন্ট কাকে বলে ?
English - what is nick point ?​

Answer 1

Explanation:

Solution−

Given integral is

\rm \: \displaystyle \int_{0}^{1} \cot ^{-1}\left(1-x+x^{2}\right)d x∫

0

1

cot

−1

(1−x+x

2

)dx

We know that

\begin{gathered}\boxed{\tt{ \: {cot}^{ - 1}x = {tan}^{ - 1} \frac{1}{x} \: }} \\ \end{gathered}

cot

−1

x=tan

−1

x

1

So, using this, we get

\rm \: = \: \displaystyle \int_{0}^{1} \tan ^{-1}\bigg[\dfrac{1}{1 - x + {x}^{2} } \bigg] d x=∫

0

1

tan

−1

[

1−x+x

2

1

]dx

\rm \: = \: \displaystyle \int_{0}^{1} \tan ^{-1}\bigg[\dfrac{1 - x + x}{1 - x + {x}^{2} } \bigg] d x=∫

0

1

tan

−1

[

1−x+x

2

1−x+x

]dx

\rm \: = \: \displaystyle \int_{0}^{1} \tan ^{-1}\bigg[\dfrac{(1 - x) + x}{1 - x(1 - x)} \bigg] d x=∫

0

1

tan

−1

[

1−x(1−x)

(1−x)+x

]dx

We know

\begin{gathered}\boxed{\tt{ \: {tan}^{ - 1} \frac{x + y}{1 - xy} = {tan}^{ - 1}x + {tan}^{ - 1}y \: }} \\ \end{gathered}

tan

−1

1−xy

x+y

=tan

−1

x+tan

−1

y

Answer 2

Answer:

The standard deviation of six observations is 4. If each observation is multiplied by 3, then the

variance of the resulting observations is

1) 12

2) 144

3) 16

4) 9To verify the properties of sides and angles of a triangle using geometric instruments.