Question

$\int_0^\pi dx =$

• A. $\frac{\pi}{2}$
• B. $-\frac{\pi}{2}$
• C. $\pi$
• D. $\frac{\pi}{4}$

Hint:

For any definite integral of $dx$ (where the integrand is 1), the result is always simply $(\text{Upper Limit} - \text{Lower Limit})$.

Answer 1

The Correct Option is C

Step 1: Find the Indefinite Integral: The integrand is implicitly 1. The integral of 1 with respect to $x$ is $x$: $$\int 1 \, dx = x$$

Step 2: Apply the Fundamental Theorem of Calculus: Evaluate the antiderivative at the upper limit ($\pi$) and lower limit ($0$): $$\int_0^\pi 1 \, dx = [x]_0^\pi\lt strong\gt Step 3: Calculate the Difference\lt /strong\gt \text{Value} = (\text{Upper Limit}) - (\text{Lower Limit})$$ $$\text{Value} = \pi - 0$$ $$\text{Value} = \pi$$ Geometrically, this represents the area of a rectangle with height 1 and width $\pi$ on the x-axis.