Question

∫ from 2 to 4 of 5 dx

Explanation:

Step1: Recall the integral rule for constant

The integral of a constant \( k \) with respect to \( x \) is \( kx + C \) (antiderivative), and for definite integral \( \int_{a}^{b} kdx=k(x)\big|_{a}^{b}=k(b - a) \). Here \( k = 5 \), \( a = 2 \), \( b = 4 \).

Step2: Apply the definite integral formula

Substitute into the formula: \( \int_{2}^{4}5dx=5x\big|_{2}^{4} \)

Step3: Evaluate the antiderivative at bounds

Calculate \( 5\times4 - 5\times2=20 - 10 = 10 \)

Answer:

\( 10 \)