- #1
keltix
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Homework Statement
definite integrals (1 + 3x) dx from (-1,5)
The Attempt at a Solution
i keep getting 6+54 but it should be 6+36
i think i might be using the wrong property
or multiplying wrong: 3[(6/n)i](6/n)
A definite integral is a mathematical concept used to find the exact area under a curve between two specific points on a graph. It is denoted by ∫ b to a f(x)dx, where a and b represent the lower and upper bounds of the integral, and f(x) is the function being integrated.
To solve a definite integral, you can use the fundamental theorem of calculus, which states that the definite integral of a function f(x) can be evaluated by finding its antiderivative F(x) and plugging in the upper and lower bounds. You can also use numerical methods or online integral calculators to find the solution.
While a definite integral has specific bounds and a definite numerical value, an indefinite integral does not have any bounds and represents a general solution in the form of a function. An indefinite integral is denoted by ∫ f(x)dx, and it can have multiple solutions with different constants of integration.
Definite integrals are used in various fields such as physics, engineering, and economics to calculate quantities such as work, displacement, area, and volume. For example, the definite integral of a velocity function can give the total distance traveled by an object.
Yes, you can approximate the value of a definite integral using numerical methods such as the trapezoidal rule or Simpson's rule. These methods use a series of calculated values from the function to approximate the area under the curve. However, for an exact solution, you will need to know the function and its antiderivative.