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Integrate the function $5xz^2+3y\cos\left(z\right)$ from 0 to $\pi $

Step-by-step Solution

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Final Answer

$24.674011z^2+3\pi y\cos\left(z\right)$
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Step-by-step Solution

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Expand the integral $\int_{0}^{\pi }\left(5xz^2+3y\cos\left(z\right)\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{\pi }5xz^2dx+\int_{0}^{\pi }3y\cos\left(z\right)dx$

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$\int_{0}^{\pi }5xz^2dx+\int_{0}^{\pi }3y\cos\left(z\right)dx$

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Learn how to solve integral calculus problems step by step online. Integrate the function 5xz^2+3ycos(z) from 0 to pi. Expand the integral \int_{0}^{\pi }\left(5xz^2+3y\cos\left(z\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{\pi }5xz^2dx results in: 24.674011z^2. The integral \int_{0}^{\pi }3y\cos\left(z\right)dx results in: 3\pi y\cos\left(z\right). Gather the results of all integrals.

Final Answer

$24.674011z^2+3\pi y\cos\left(z\right)$

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 (5x+3y)dx from 0 to \pi using basic integralsSolve integral of (5x+3y)dx from 0 to \pi using u-substitutionSolve integral of (5x+3y)dx from 0 to \pi using integration by partsSolve integral of (5x+3y)dx from 0 to \pi using tabular integration

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Function Plot

Plotting: $5xz^2+3y\cos\left(z\right)$

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7
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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: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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