Answer to Question #222030 in Calculus for Anjanu

Question

Integrate ln(2x+2) from -1<=x<=1

Answer 1

$\int$_-1 ¹ ln(2x+2) dx

Let 2x + 2 = 2t ..................Equation(1)

Differentiating both the sides we have

dx = dt and x varies from -1 $\rightarrow$ 1 so by using Equation(1) t varies from 0 $\rightarrow$ 2

Now the integral takes the form

$\int$₀ ² ln(2t) dt

By using integration by parts and considering u = ln(2t) and v = 1, we have

[ ln(2t) t - $\int$ $\dfrac{2}{2t}$ . t dt ]₀ ²

[ ln(2t) t - $\int$ 1 dt ]₀ ²

[ ln(2t) t - t ]₀ ²

On substituting the limits

2[ ln (4 )- 1]