# Mathematics for JEE Main

## Area Between Many Curves

Area Under Curve Tutorial Area Of The Region Bounded By Several Curves Consider the figure given in the thumbnail. Three continuous Curves f(x), g(x), and h(x) defined in the intervals [a, b], [a, c], and [c, b] respectively and intesect each other at ‘A’, ‘B’, and ‘C’. Now the area of the shaded region SACBA …

## Area Between Two Curves3

Area Under Curve Tutorial Area Between Two Curves Using Horizontal Strip Let x = F(y) and x = G(y) are two continuous functions such that F(y) ≥ G(y), where y ∈ [c, d]. These two curves intersect each other at y = b. Now the area bounded by these two curves from y = c …

## AUC Using Horizontal Strip

Area Under Curve Tutorial Area Under Curves Concept of Horizontal Strip While calculating the area of a region we are using the concept of vertical stip so far. But in some cases, it has been observed that the calculating area of a region bounded by the curve(s) along with some additional condition would be much …

## Area Between Two Curves2

Area Under Curve Tutorial Area Enclosed Between Two Intersecting Curves Now we are going to find the area of the regions enclosed between two intersecting curves that are intersecting each other at the finite numbers of intervals. In these intervals they have behaviour like f(x)≥g(x) and g(x)≥f(x). In such conditions, we have to calculate the …

## Area Between Two Curves1

Area Under Curve Tutorial Area Between Two Non Intersecting Curves Let f(x) and g(x) are two continuous functions in the interval [a, b] such that f(x)≥g(x) for every x∈[a, b]. Then the area of the region bounded between f(x) and g(x) will be the area of the region below the function f(x) and above the …

## AUC function Changes Sign

Area Under Curve Tutorial Area Under The Curves When Function Changes Sign (f(x)≥0, f(x)≤0) In this tutorial we will learn how to find the area of the region bounded by the continuous function which changes its sign. That means there will be a finite number of intervals in which the sign of the function may …

## AUC f(x)≤0

Area Under Curve Tutorial Area Bounded By Non Positive Function The Definite Integration of a non positive function f(x) with respect to ‘x’ from ‘a’ to ‘b’ gives the area of the shaded region, given in above figure. Let f(x) be a non positive countinuous function on an interval [a, b], such that f(x)≤0. Then …