Area - Important Formulae of the Area - Area Bounded By Curve

Area - Area Bounded By Curve

The area bounded by the continuous curve y = f(x), the axis of x and the ordinates x = a and x = b (where b>a and

$F(x)\geq \, 0\, \forall x\, \in [a,b])$ is given by

$A\, =\, \int ^{c}_{a} {f(x)dx\, =\, \int ^{b}_{a} {f(x)\, dx}}$

The area bounded by the continuous curve y = f(x), the axis of x and the ordinates x = a and x = b (where b>a and

If the curve cross the x- axis at (c, 0) then the area bounded by the curve y = f(x)and the coordinate x = a x = b(b > a and a < c < b) is given by

$A\, =\, \int ^{b}_{a} {f(x)dx\, \, \, \, and\, A\, =\, \int ^{b}_{a} {f(x)\, dx}}\, \, \, if\, f(x)\leq 0$

If the curve cross the x- axis at (c, 0) then the area bounded by the curve y = f(x)and the coordinate x = a x = b(b > a and a < c < b) is given by

When two curves y =f (x) and y =g (x) intersect, the bounded area

$A\, =\, \int ^{b}_{a} {[g(x)-f(x)]}dx$

where and b are roots of equation f(x)  g(x) where $g(x)\geq f(x)\forall x\in [a,b]$

When two curves y =f (x) and y =g (x) intersect, the bounded area

The area bound by the straight lines x=a, x=b(a < b) and the curves y=f(x) andy=g(x) Provided f(x)<g(x (a<= x<=b), is given by

$A\, =\, \int ^{b}_{a} {[g(x)-f(x)]}dx$

The area bound by the straight lines x=a, x=b(a < b) and the curves y=f(x) andy=g(x) Provided f(x)<g(x (a<= x<=b), is given by

Formulae :

The area of rhombus formed by $ax\pm by\pm c\, =0$ is

$\frac {2{c}^{2}} {|ab|}\, \, \, \, sq.\, units$

2. The area of the region bounded by |x| + |y | =. a is. 2a*a sq.units

3. The area of the triangle formed by the lines $y\, =\, {m}_{1}x+{c}_{1},y\, =\, {m}_{2}x+{c}_{2},\, \, y\, =\, {m}_{3}x+{c}_{3}$ is

$\frac {1} {2}|\sum {\frac {{(c1-c2)}^{2}} {m1-m2}}\, \, \, sq.\, units$

4. The area of the parallelogram formed by a1x+ b1y +c1 = 0, a1x + b1y +d1 = 0, a2x. + b2y + c2 = 0,a2x + b2y + d2 = 0. is

$|\frac {(c1-d1)(c2-d2)} {a1b1+a2b2}|\, \, sq\, units$

5. Area of ther egion bounded by y = ax2 + bx + c. and x -axis is $\frac {{({b}^{2}-4ac)}^{3/3}} {{6a}^{2}}$

Post By : Rahul Kumar 09 Apr, 2020 1570 views Maths