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Integrate the function $\sqrt{1+x^2}$ from $-1$ to $1$

Used Formulas

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sinh
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asinh
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atanh
acoth
asech
acsch

Derivatives of trigonometric functions

· Derivative of secant function
$\frac{d}{dx}\left(\sec\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)\tan\left(\theta \right)$

Basic Derivatives

· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Trigonometric Integrals

$\int\sec\left(\theta \right)^2dx=\tan\left(\theta \right)+C$
$\int\sec\left(\theta \right)^ndx=\frac{\sin\left(\theta \right)\sec\left(\theta \right)^{\left(n-1\right)}}{n-1}+\frac{n-2}{n-1}\int\sec\left(\theta \right)^{\left(n-2\right)}dx$
$\int\sec\left(\theta \right)dx=\ln\left(\sec\left(\theta \right)+\tan\left(\theta \right)\right)+C$

Integration Techniques

· Integration by Parts
$\int udv=uv - \int vdu$

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Function Plot

Plotting: $\sqrt{1+x^2}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

7. See formulas

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