Question

Find the value of ∫ Cos x + x dx.

Answer 1

$\huge \fbox{ \underline \purple{Answer }}$

Solution:

∫ Cos x + x dx

= ∫ Cos x dx + ∫ x dx

∫cosx dx=sin x+C}

∫x^ndx=x^n+1/n+1

= sin x + x²/2 + C

#thats all it is quite simple

Answer 2

Answer:

sin x + x²/2 + c is the answer.

Concept:

Indefinite integration.

Integration: In maths, integration is defined as the addition or summing up of something to find the total. Its reverse operation is called differentiation.

In indefinite integration, we are not given the values of variables while in definite integration we are provided with limits to put into the function.

Find:

$\int (cos \ x + x) dx$

Solution:

Let I = $\int (cos \ x + x) dx$

Separating the terms, we get

I = ∫ cos x dx + ∫  x dx

as we know, ∫  cos x dx = sin x + c

and ∫ xⁿ dx = (xⁿ⁺¹/n+1) + c

So, now we have,

I = sin x + (x¹⁺¹/1 + 1) + c

where c is an integration constant.

I = sin x + x²/2 + c

Hence, ∫ (cos x + x)dx  = sin x + x²/2 + c.

#SPJ3