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Integrate the function $\sqrt[3]{2}\left(3z+3\right)$ from $3$ to $9$

Step-by-step Solution

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Solution

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Final Answer

$158.750052$
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Step-by-step Solution

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Calculate the power $\sqrt[3]{2}$

$\int_{3}^{9}\sqrt[3]{2}\left(3z+3\right)dz$

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

$\int_{3}^{9}\sqrt[3]{2}\left(3z+3\right)dz$

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Learn how to solve definite integrals problems step by step online. Integrate the function (3z+3)2^1/3 from 3 to 9. Calculate the power \sqrt[3]{2}. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Expand the integral \int_{3}^{9}\left(3z+3\right)dz into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product \sqrt[3]{2}\left(\int_{3}^{9}3zdz+\int_{3}^{9}3dz\right).

Final Answer

$158.750052$

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 (3z+3)2^0.3333dz from 3 to 9 using partial fractionsSolve integral of (3z+3)2^0.3333dz from 3 to 9 using basic integralsSolve integral of (3z+3)2^0.3333dz from 3 to 9 using u-substitutionSolve integral of (3z+3)2^0.3333dz from 3 to 9 using integration by partsSolve integral of (3z+3)2^0.3333dz from 3 to 9 using trigonometric substitution

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Function Plot

Plotting: $\sqrt[3]{2}\left(3z+3\right)$

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a
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y
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(◻)
+
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◻/◻
/
÷
◻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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