There is no substitution required (although that would yield the same answer).jimen113 said:If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?
jimen113 said:If x=3t, then
dt=3
integral of sin x is -cos x
Is this correct?
A definite integral is a mathematical concept that represents the area under a curve between two points on a graph. It is denoted by the symbol ∫ and is used to calculate the total accumulation of a function over a specific interval.
To evaluate a definite integral, you need to first determine the limits of integration (the two points on the graph) and then use the fundamental theorem of calculus to find the antiderivative of the function. Next, substitute the limits of integration into the antiderivative and calculate the resulting value.
A definite integral has specific limits of integration and results in a single numerical value, while an indefinite integral does not have limits of integration and results in a function. In other words, a definite integral gives a specific answer, while an indefinite integral gives a family of answers.
Definite integrals are used in many fields of science and engineering, such as physics, economics, and statistics. They can be used to calculate areas, volumes, and other physical quantities, as well as to model real-world phenomena like population growth and changes in stock prices.
Yes, definite integrals can be evaluated using numerical methods such as the trapezoid rule, Simpson's rule, and Monte Carlo integration. These methods are used when the function is too complex to find an exact solution or when the limits of integration are difficult to work with.