Sentences with DEFINITE-INTEGRAL
Check out our example sentences below to help you understand the context.Sentences
1
"The definite integral of a function f(x) over the interval [a, b] represents the area between the graph of f(x) and the x-axis."
2
"To evaluate a definite integral, we use the limit of a Riemann sum as the number of subintervals approaches infinity."
3
"The fundamental theorem of calculus states that the definite integral of a function f(x) can be found by evaluating its antiderivative at the endpoints of the interval."
4
"The definite integral of a constant function over any interval is equal to the product of the constant and the width of the interval."
5
"The definite integral of a function can be interpreted as the net area enclosed by the graph of the function and the x-axis."
6
"The properties of definite integrals allow for the calculation of areas, volumes, and other quantities in mathematics and physics."
7
"The definite integral of a positive function on an interval gives the area under the curve."
8
"The definite integral of a negative function on an interval gives the negative of the area under the curve."
9
"The definite integral of a function can be approximated using numerical methods such as the trapezoidal rule or Simpson's rule."
10
"A definite integral may have different values depending on the limits of integration."
11
"The definite integral of a function is sometimes denoted by the symbol ∫."
12
"The definite integral of a function represents the accumulated sum of its values over an interval."
13
"The definite integral of a function with respect to x gives the total change in the antiderivative of the function over the interval."
14
"The definite integral of a function may not exist if the function is not defined or is not integrable on the interval."
15
"The definite integral of a function can be used to find the average value of the function over an interval."
16
"The definite integral of a function over an interval can be split into multiple integrals over subintervals."
17
"The definite integral of a function can be used to calculate the displacement of an object given its velocity."
18
"The definite integral of a function can be used to calculate the total mass of an object given its density."
19
"The definite integral of a function can be used to calculate the work done in moving an object against a force."
20
"The definite integral of a function can be used to calculate the length of a curve in a coordinate system."
1
"To find the area under a curve, you need to evaluate the definite integral of the function."
2
"The definite integral of a constant function is equal to the product of the function's value and the width of the interval."
3
"The definite integral represents the accumulation of an infinitesimal quantity over a given interval."
4
"By applying the fundamental theorem of calculus, we can calculate definite integrals by finding antiderivatives."
5
"The definite integral of a function may be negative if the function dips below the x-axis within the interval of integration."
6
"When using numerical methods, such as Simpson's rule, to approximate a definite integral, we partition the interval into subintervals."
7
"The definite integral is often used to solve problems involving rates of change, such as computing the displacement of an object given its velocity function."
8
"In physics, the area under a velocity-time graph represents the displacement, which can be found by evaluating the definite integral of the graph."
9
"To calculate the total cost of production, we can represent the cost function as a definite integral of the rate of production function."
10
"The notion of a definite integral was introduced by mathematicians in the late 17th century."
