# Integrate tan(x) from 0 to pi/2

## \int_{0}^{\frac{\pi}{2}}\tan\left(x\right)dx

Go!
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0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$37.3319$

## Step by step solution

Problem

$\int_{0}^{\frac{\pi}{2}}\tan\left(x\right)dx$
1

The integral of the tangent function is given by the following formula, $\displaystyle\int\tan(x)dx=-\ln(\cos(x))$

$\left[-\ln\left(\cos\left(x\right)\right)\right]_{0}^{\sqrt{2}}$
2

Evaluate the definite integral

$\ln\left(\cos\left(1.5708\right)\right)\left(-1\right)-1\cdot \ln\left(\cos\left(0\right)\right)\left(-1\right)$
3

Multiply $-1$ times $-1$

$\ln\left(\cos\left(0\right)\right)\cdot 1+\ln\left(\cos\left(1.5708\right)\right)\left(-1\right)$
4

Calculating the cosine of $\sqrt{2}$ degrees

$\ln\left(1\right)\cdot 1+\ln\left(6.12\times 10^{-17}\right)\left(-1\right)$
5

Calculating the natural logarithm of $0$

$0\cdot 1-37.3319\left(-1\right)$
6

Any expression multiplied by $0$ is equal to $0$

$0-37.3319\left(-1\right)$
7

Multiply $-1$ times $-37.3319$

$0+37.3319$
8

Add the values $37.3319$ and $0$

$37.3319$

$37.3319$

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### Main topic:

Integral calculus

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