Question

The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate the following integral:

∫[0, b] f(x)dx

Answer 1

The integral ∫[0, b] f(x)dx represents the area of the regions bounded by the graph of f and the x-axis from x = 0 to x = b.

Step-by-step explanation:

In calculus, the definite integral ∫[0, b] f(x)dx is a mathematical expression that signifies finding the area under the curve of the function f(x) from x = 0 to x = b.

To evaluate this integral, one would typically find the antiderivative of the function f(x) and then substitute the upper limit (b) and the lower limit (0) into this antiderivative. The difference between these two values provides the area of the region bounded by the graph of f and the x-axis within the specified interval.

Understanding definite integrals is crucial for determining accumulated quantities, such as area or total accumulated change, represented by a given function over a specific range.

Question:

The figure to the right shows the area of regions bounded by the graph of ( f ) and the x-axis. Evaluate the following integral:

`\[ \int_(0)^(b) f(x) \, dx \]`