What is the integral from-1 to 1 of 2/(sqrt(x+1)) ?

The integral from-1 to 1 of 2/(sqrt(x+1)) is 4sqrt(2)

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integral from-1 to 1 of 2/(sqrt(x+1))

\int_{- 1}^{1} \frac{2}{x + 1} d x

42

Decimal

5.65685 \dots

Solution steps

\int_{- 1}^{1} \frac{2}{x + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{- 1}^{1} \frac{1}{x + 1} d x

Apply u-substitution

: \int_{0}^{2} 2 d u

= 2 \cdot \int_{0}^{2} 2 d u

Integral of a constant:

\int a d x = a x

= 2 [2 u]_{0}^{2}

Compute the boundaries:

22

= 2 \cdot 22

Simplify

= 42

x^{2} - 3, y = 0, - 2, 2

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{7}{2}}} d x

f (x) = 5 sin (x) cos (x)

(x, y) \to (π, 3) lim (\frac{y cos ( 2 x )}{y + cos ( x )})

\int e^{c o s (10 t)} sin (10 t) d t

What is the integral from-1 to 1 of 2/(sqrt(x+1)) ?
The integral from-1 to 1 of 2/(sqrt(x+1)) is 4sqrt(2)