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Integrate the function $36-\left(6-\sqrt{36+\frac{-36x^2}{64}}\right)$ from 0 to $8$

Step-by-step Solution

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Solution

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Final Answer

$277.699112$
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Step-by-step Solution

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Take $\frac{-36}{64}$ out of the fraction

$\int_{0}^{8}\left(36-\left(6-\sqrt{36-\frac{9}{16}x^2}\right)\right)dx$

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

$\int_{0}^{8}\left(36-\left(6-\sqrt{36-\frac{9}{16}x^2}\right)\right)dx$

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Learn how to solve definite integrals problems step by step online. Integrate the function 36-(6-(36+(-36x^2)/64)^1/2) from 0 to 8. Take \frac{-36}{64} out of the fraction. Solve the product -\left(6-\sqrt{36-\frac{9}{16}x^2}\right). Simplify the expression inside the integral. The integral \int_{0}^{8}30dx results in: 240.

Final Answer

$277.699112$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (36+-1(6+-1(36+-36x^2/64)^0.5))dx from 0 to 8 using partial fractionsSolve integral of (36+-1(6+-1(36+-36x^2/64)^0.5))dx from 0 to 8 using basic integralsSolve integral of (36+-1(6+-1(36+-36x^2/64)^0.5))dx from 0 to 8 using u-substitutionSolve integral of (36+-1(6+-1(36+-36x^2/64)^0.5))dx from 0 to 8 using integration by partsSolve integral of (36+-1(6+-1(36+-36x^2/64)^0.5))dx from 0 to 8 using trigonometric substitution

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Function Plot

Plotting: $36-\left(6-\sqrt{36+\frac{-36x^2}{64}}\right)$

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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
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: 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

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