Solve Integral Equation Problems
Integration is differ from differentiation in geometry and other application of integral calculus it becomes necessary to find difference in values of an integral of a function f(x)for two assigned values of independent variable.
∫f(x) dx = F(x)
The function f(x) is called Integrand.The variable x in dx is said to be variable of integration or integrator.The process of finding the integral is called integration.
Looking out for more help on definite integral in algebra by visiting listed websites.
solve integral equation problems:
In integration Let y = f(x) be a continuous function defined on [a, b], which is positive (f(x) lies on or above x-axis) on the interval [a, b]. Then,integration for the area bounded by the curve y = f(x), the x-axis and the ordinates x = a and x = b is given by
Area=`int_a^bf(x)dx` (or)`int_a^bydx`
If f(x) ≤ 0 (f(x) lies on or below x-axis) for all x in a ≤ x ≤ b then area is given by
Area =`int_a^b(-y)dx`
=`int_a^b(-f(x))dx`
Example - solve integral equation problems :
Find the area of region bounded by the line 3x − 2y + 6 = 0,x = 1, x = 3 and x-axis.
Solution :
Since the line 3x − 2y + 6 = 0 lies above the x-axis in the interval [1, 3], (i.e., y > 0 for x ∈ (1,3)) integration for the required area
A =`int_1^3ydx`
=3/2 `int_1^3(x+2)dx`
=3/2[x^2+2x]31
=3/2[1/2(9-1)+2(3-1)]
=3/2(4+4)
=12 sq.units
Between, if you have problem on these topics Indefinite Integral Examples, please browse expert math related websites for more help on neet 2014.
Example - solve integral equation problems:
Integrate ∫(x^3+2)/(x-1)
Solution :
=∫(x^3-1+3)/(x-1) dx =∫((x^3-1)/(x-1)+3/(x-1))dx
=∫((x-1)(x^2+x+1))/(x-1)+3/(x-1))dx
=∫((x^2+x+1)+(3/(x-1)))dx
=x^3/3+x^2/2+x+3 log(x-1)+c.
Practice problem - solve integral equation problems:
Problem 1:
integrate∫(x^2-5x+1)/x dx.
Answer: x^2-5x+log x+c.
Problem 2:
Find the area of region bounded by the line 3x − 5y − 15 = 0, x = 1,x = 4 and x-axis.
Answer: 9/2 sq. units.
∫f(x) dx = F(x)
The function f(x) is called Integrand.The variable x in dx is said to be variable of integration or integrator.The process of finding the integral is called integration.
Looking out for more help on definite integral in algebra by visiting listed websites.
solve integral equation problems:
In integration Let y = f(x) be a continuous function defined on [a, b], which is positive (f(x) lies on or above x-axis) on the interval [a, b]. Then,integration for the area bounded by the curve y = f(x), the x-axis and the ordinates x = a and x = b is given by
Area=`int_a^bf(x)dx` (or)`int_a^bydx`
If f(x) ≤ 0 (f(x) lies on or below x-axis) for all x in a ≤ x ≤ b then area is given by
Area =`int_a^b(-y)dx`
=`int_a^b(-f(x))dx`
Example - solve integral equation problems :
Find the area of region bounded by the line 3x − 2y + 6 = 0,x = 1, x = 3 and x-axis.
Solution :
Since the line 3x − 2y + 6 = 0 lies above the x-axis in the interval [1, 3], (i.e., y > 0 for x ∈ (1,3)) integration for the required area
A =`int_1^3ydx`
=3/2 `int_1^3(x+2)dx`
=3/2[x^2+2x]31
=3/2[1/2(9-1)+2(3-1)]
=3/2(4+4)
=12 sq.units
Between, if you have problem on these topics Indefinite Integral Examples, please browse expert math related websites for more help on neet 2014.
Example - solve integral equation problems:
Integrate ∫(x^3+2)/(x-1)
Solution :
=∫(x^3-1+3)/(x-1) dx =∫((x^3-1)/(x-1)+3/(x-1))dx
=∫((x-1)(x^2+x+1))/(x-1)+3/(x-1))dx
=∫((x^2+x+1)+(3/(x-1)))dx
=x^3/3+x^2/2+x+3 log(x-1)+c.
Practice problem - solve integral equation problems:
Problem 1:
integrate∫(x^2-5x+1)/x dx.
Answer: x^2-5x+log x+c.
Problem 2:
Find the area of region bounded by the line 3x − 5y − 15 = 0, x = 1,x = 4 and x-axis.
Answer: 9/2 sq. units.