Question

integrate [x]+[x^2] from 0 to 1.5

Answer 1

integrate [x]+[x^2] from 0 to 1.5

Integral of variable equals: $\int x \, dx = \frac{x^2}{2}$

Integral of square equals: $\int x^2 \, dx = \frac{x^3}{3}$

Fundamental theorem of calculus:

$$\int_{a}^{b} f(x) \, dx = F(b) - F(a)$$

F(x) – integral of f(x).

Therefore:

$$\int_{0}^{1.5} (x + x^2) \, dx = \frac{x^2}{2} \int_{0}^{1.5} + \frac{x^3}{3} \int_{0}^{1.5} = \frac{1.5^2}{2} - 0 + \frac{1.5^3}{3} - 0 = 2.25$$

Answer: 2.25