calculus problems

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..

If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..

Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..

Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..

If f (x) is a function continuous on [a, b] then Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(b) ..

Because of these condition, the 2 n d order differential equation y''= 2 has particular solution x 2 + x + 2. The values f (0) = 2 and f '(0) = 1 are called initial values. The problem of finding the solution of a differential equation that satisfies these prescribed initial conditions is..

..

Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a heavy meteorite e..