Integrate the function $\left(1738-1.523x\right)\left(1-\cos\left(\frac{\pi x}{2\cdot 600}\right)\right)$ from 0 to $600$

Step-by-step Solution

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Final answer to the problem

$\frac{5.24\times 10^{-3}}{1.51\times 10^{-26}}$
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Step-by-step Solution

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Simplifying

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$\int_{0}^{600}\left(1738-1.523x\right)\left(1-\cos\left(\frac{\pi x}{1200}\right)\right)dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function (1738-1.523x)(1-cos((pix)/(2*600))) from 0 to 600. Simplifying. Take \frac{\pi }{1200} out of the fraction. Rewrite the integrand \left(1738-1.523x\right)\left(1-\cos\left(2.62\times 10^{-3}x\right)\right) in expanded form. Expand the integral \int_{0}^{600}\left(1738-1738\cos\left(2.62\times 10^{-3}x\right)-1.523x+1.523x\cos\left(2.62\times 10^{-3}x\right)\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$\frac{5.24\times 10^{-3}}{1.51\times 10^{-26}}$

Exact Numeric Answer

$346188275887333750000000$

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Function Plot

Plotting: $\left(1738-1.523x\right)\left(1-\cos\left(\frac{\pi x}{2\cdot 600}\right)\right)$

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

See formulas (8)

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