Question

) Evaluate the following integral:
(1) for sin x dx (11) { x dx
[Ans: (1) 1, (ii) 12]
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Answer 1

Answer:

1.$-cos x+C$

2.$\frac{x^2}{2}$

Step-by-step explanation:

We are given that two functions '

1.sinx 2. x

We have to evaluate  the integral.

We know that

$\int sinx dx= -cosx +C$

Where C=Integration constant

Therefore , $\int sinxdx=-cos x+C$

2.We know that

$\int x^n dx=\frac{x^{n+1}}{n+1}+C$

Using the formula

$\int xdx=\frac{x^2}{2}+C$

Answer 2

Given:

$\bold{i) \int \sin x dx}\\\\\bold{ii) \int x dx}$

To find:

Evaluate the integral.

Solution:

Formula:

$\int x^n dx= \frac{x^{n+1}}{n+1} + c\\\\\int sin \ x \ dx = -cos x +c$

i)

$\to \int \sin x dx\\\\\to \int \sin x dx = -\cos x+c$

ii)

$\to \int x \ dx=\int x^1 dx$

              $= \frac{x^{1+1}}{1+1}\\\\ = \frac{x^2}{2}+c$