Integration Review

Front

What is the integral of a function?

Back

The integral of a function represents the area under the curve of that function on a given interval.

Front

What is the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x) dx = F(b) - F(a).

Front

What does ∫2x + 4 dx equal?

Back

x² + 4x + c, where c is the constant of integration.

Front

How do you estimate the area under a curve using Riemann sums?

Back

You divide the interval into subintervals, calculate the area of rectangles formed by the function values at specific points, and sum these areas.

Front

What is the difference between RRAM and LRAM?

Back

RRAM (Right Riemann Sum) uses the right endpoint of each subinterval to determine the height of rectangles, while LRAM (Left Riemann Sum) uses the left endpoint.

Front

What is the area bounded by a function and the x-axis?

Back

The area bounded by a function and the x-axis can be found by integrating the function over the specified interval, taking into account the sign of the function.

Front

What does the notation ∫_a^b f(x) dx represent?

Back

It represents the definite integral of the function f(x) from the lower limit a to the upper limit b.

Front

What is an antiderivative?

Back

An antiderivative of a function f is a function F such that F' = f, meaning the derivative of F is f.

Front

What is the significance of the constant 'c' in indefinite integrals?

Back

The constant 'c' represents the family of all antiderivatives of a function, as the derivative of a constant is zero.

Front

How do you find the area under a curve using definite integrals?

Back

You calculate the definite integral of the function over the interval, which gives the net area between the curve and the x-axis.