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Integrate the function $\frac{1-\cos\left(g\right)}{g^2}$ from $x$ to $1$

Step-by-step Solution

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Final Answer

$0.486385+\frac{1}{x}+\frac{x^7}{35280}+\frac{-x^5}{600}+\frac{x^3}{18}-x+\frac{-\cos\left(x\right)}{x}$
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Step-by-step Solution

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Expand the fraction $\frac{1-\cos\left(g\right)}{g^2}$ into $2$ simpler fractions with common denominator $g^2$

$\int_{x}^{1}\left(\frac{1}{g^2}+\frac{-\cos\left(g\right)}{g^2}\right)dg$

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$\int_{x}^{1}\left(\frac{1}{g^2}+\frac{-\cos\left(g\right)}{g^2}\right)dg$

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Learn how to solve definite integrals problems step by step online. Integrate the function (1-cos(g))/(g^2) from x to 1. Expand the fraction \frac{1-\cos\left(g\right)}{g^2} into 2 simpler fractions with common denominator g^2. Simplify the expression inside the integral. The integral \int_{x}^{1}\frac{1}{g^2}dg results in: -1+\frac{1}{x}. Gather the results of all integrals.

Final Answer

$0.486385+\frac{1}{x}+\frac{x^7}{35280}+\frac{-x^5}{600}+\frac{x^3}{18}-x+\frac{-\cos\left(x\right)}{x}$

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Function Plot

Plotting: $\frac{1-\cos\left(g\right)}{g^2}$

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5
6
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

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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

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