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Integrate $\int3y\sqrt{7-3y^2}dy$

Step-by-step Solution

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Final Answer

$-\frac{1}{3}\sqrt{\left(7-3y^2\right)^{3}}+C_0$
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Step-by-step Solution

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The integral of a function times a constant ($3$) is equal to the constant times the integral of the function

$3\int y\sqrt{7-3y^2}dy$

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$3\int y\sqrt{7-3y^2}dy$

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Learn how to solve problems step by step online. Integrate int(3y(7-3y^2)^1/2)dy. The integral of a function times a constant (3) is equal to the constant times the integral of the function. First, factor the terms inside the radical by 3 for an easier handling. Taking the constant out of the radical. We can solve the integral 3\int\sqrt{3}y\sqrt{\frac{7}{3}-y^2}dy by applying integration method of trigonometric substitution using the substitution.

Final Answer

$-\frac{1}{3}\sqrt{\left(7-3y^2\right)^{3}}+C_0$

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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 3ydy using partial fractionsSolve integral of 3ydy using basic integralsSolve integral of 3ydy using u-substitutionSolve integral of 3ydy using integration by partsSolve integral of 3ydy using trigonometric substitution

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Function Plot

Plotting: $-\frac{1}{3}\sqrt{\left(7-3y^2\right)^{3}}+C_0$

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1
2
3
4
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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