Questions: ∫ from 0 to 10 of x^2 + x + 1 dx

Transcript text: \(\int_{0}^{10} x^{2}+x+1 d x\)

Solution

Solution Steps

To solve the definite integral of the function \( f(x) = x^2 + x + 1 \) from 0 to 10, we can use numerical integration methods provided by Python libraries such as scipy.

Step 1: Define the Integral

We need to evaluate the definite integral of the function \( f(x) = x^2 + x + 1 \) from 0 to 10. This can be expressed as: \[ \int_{0}^{10} (x^2 + x + 1) \, dx \]

Step 2: Compute the Integral

Using numerical integration methods, we find the value of the integral: \[ \int_{0}^{10} (x^2 + x + 1) \, dx = 393.3333 \]