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Find the integral $x\int_{2}^{\sqrt{2}} e^{-t^2}dt$

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Solving: $x\int_{2}^{\sqrt{2}} e^{-t^2}dt$
Solve instead: $x\int_2^{\sqrt{2}}\left(e^{-t^2}\right)dx$

Solution

Formulas

Videos

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Finding specific antiderivatives: rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=bjdOWH43-9s

Definite integral of trig function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=ldLdWj6DLTw

Integral of 1/sqrt(1-x^2)

https://www.youtube.com/watch?v=9AvyXgfNN9E

Triple integrals 2 | Double and triple integrals | Multivariable Calculus | Khan Academy

https://www.youtube.com/watch?v=vxQvL_WhBGU

Function Plot

Plotting: $\frac{\sqrt{\pi }\mathrm{erf}\left(\sqrt{2}\right)x}{2}-\frac{\sqrt{\pi }\mathrm{erf}\left(2\right)x}{2}+C_0$

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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Used Formulas

See formulas (2)

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