Integrate the function $\frac{4}{5}x^3+2x^2-x$ from 0 to $1$

Step-by-step Solution

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Final answer to the problem

$\frac{2}{3}-\frac{1}{2}$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Expand the integral $\int_{0}^{1}\left(\frac{4}{5}x^3+2x^2-x\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{1}\frac{4}{5}x^3dx+\int_{0}^{1}2x^2dx+\int_{0}^{1}-xdx$

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$\int_{0}^{1}\frac{4}{5}x^3dx+\int_{0}^{1}2x^2dx+\int_{0}^{1}-xdx$

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Learn how to solve definite integrals problems step by step online. Integrate the function 4/5x^3+2x^2-x from 0 to 1. Expand the integral \int_{0}^{1}\left(\frac{4}{5}x^3+2x^2-x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1}\frac{4}{5}x^3dx results in: 0. The integral \int_{0}^{1}2x^2dx results in: \frac{2}{3}. The integral \int_{0}^{1}-xdx results in: -\frac{1}{2}.

Final answer to the problem

$\frac{2}{3}-\frac{1}{2}$

Exact Numeric Answer

$0.166667$

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Function Plot

Plotting: $\frac{4}{5}x^3+2x^2-x$

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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

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 (2)

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