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# Integrate the function $\frac{498081.522}{\sqrt{x^{7}}}$ from $1$ to $\frac{2}{5}$

## Step-by-step Solution

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$551251.607309$
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##  Step-by-step Solution 

Problem to solve:

$\int_{1}^{\frac{2}{5}}\frac{498081.522}{\sqrt{x^{7}}}dx$

Specify the solving method

1

Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: $\int_a^bf(x)dx=-\int_b^af(x)dx$

$-\int_{\frac{2}{5}}^{1}\frac{498081.522}{\sqrt{x^{7}}}dx$

Learn how to solve definite integrals problems step by step online.

$-\int_{\frac{2}{5}}^{1}\frac{498081.522}{\sqrt{x^{7}}}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function 498081.522/(x^7/5) from 1 to 2/5. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. The integral of a function times a constant (498081.522) is equal to the constant times the integral of the function. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -\frac{7}{5}.

$551251.607309$

##  Explore different ways to solve this problem

SnapXam A2

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5
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7
8
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
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

### Main topic:

Definite Integrals

~ 0.05 s

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