The value of _(-2)^3, x-1, dx is Option 1: 5/2 Option 2: -5/2 Option 3: 13/2 Option 4: 13

Answer: 13/2. Solution: Split at x=1 where the modulus changes sign. _(-2)^1(1-x)dx=92 and _1^3(x-1)dx=2. Adding gives 92+2=13/2.

Calculus

Integrals

Easy

common

The value of $\int_{-2}^{3} |x-1|\, dx$ is

5/2

-5/2

13/2

✅ Correct Option: 3

Split at $x=1$ where the modulus changes sign. $\int_{-2}^{1}(1-x)dx=\frac92$ and $\int_{1}^{3}(x-1)dx=2$ . Adding gives $\frac92+2=\frac{13}{2}$ .

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