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Integrate the function $x-1$ from $-1$ to $2$

Step-by-step Solution

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Solution

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Final Answer

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

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We could not solve this problem by using the method: Integrate by trigonometric substitution

1

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

$\int_{-1}^{2} xdx+\int_{-1}^{2}-1dx$

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

$\int_{-1}^{2} xdx+\int_{-1}^{2}-1dx$

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

Final Answer

$-\frac{3}{2}$

Exact Numeric Answer

$-1.5$

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 (x-1)dx from -1 to 2 using partial fractionsSolve integral of (x-1)dx from -1 to 2 using basic integralsSolve integral of (x-1)dx from -1 to 2 using u-substitutionSolve integral of (x-1)dx from -1 to 2 using integration by parts

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Function Plot

Plotting: $x-1$

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a
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x
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

How to improve your answer:

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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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