Introduction for reviewing calculus:-
The process of summarizing the calculus like over viewing the important concepts and problems in calculus are referred as reviewing calculus. Calculus is a measure of how a given function changes as its input change. Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus is widely used in science and engineering since many of the things we are studying (like velocity, acceleration, and current in a circuit) do not perform in a simple, linear fashion. While reviewing calculus we shall discuss types of calculus along with an example.
Types of Calculus for Reviewing:
Differential calculus
Differential calculus is used to find the rate of change of a quantity
Integral calculus
Integral calculus is used to find the quantity where the rate of change is known
Integral calculus and Differential calculus perform inverse operation they are just opposite to each other
Example Problems for Reviewing:
Integral Calculus Sample Problems for reviewing
Problem 1:
Find the integral of the given equation 6x2+18x dx
Solution:
?6x2+18x dx = ?6x2 dx +?18x dx
Integrating the above equation
We get
=6x3/3 + 18x2/2
Now simplifying the above equation we get
=2x3+ 9x2
Problem 2:
Integrate the following expression 2ex + 13ex .
Solution:
The expression is 2ex + 13ex
= ? 2ex+ 13 ex dx
= ? 2 ex dx + ? 13 ex dx
By integrating the above, we get as follows
= 2ex+ 13 ex + c.
Differential Calculus Sample Problems for reviewing
Find the gradient of
(I) the tangent (ii) the normal
To the curve y = 2x3 - 4x2 at the point (2, 3)
Solution:-
The given equation is y = 2x3 - 4x2
The given point (2, 3).
m1 = dy/dx
dy /dx = d/dx (2x3 - 4x2)
= 6x2 – 8x.
The slope of the tangent is dy/dx at x = 2
dy / dx at x = 2 is
dy/ dx = 6(2) 2 – 8(2)
= 24 – 16
m1 = 8
The slope of the normal is found using m1 × m2 = -1.
m1* m2 = -1
Plugging in the value of m1 in the m1 × m2 = -1.
We get
8 * m2 = -1
Now divide it by 8 on both sides
8 *m2 / 8= -1 / 8
m2 = - 1 / 8
The process of summarizing the calculus like over viewing the important concepts and problems in calculus are referred as reviewing calculus. Calculus is a measure of how a given function changes as its input change. Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus is widely used in science and engineering since many of the things we are studying (like velocity, acceleration, and current in a circuit) do not perform in a simple, linear fashion. While reviewing calculus we shall discuss types of calculus along with an example.
Types of Calculus for Reviewing:
Differential calculus
Differential calculus is used to find the rate of change of a quantity
Integral calculus
Integral calculus is used to find the quantity where the rate of change is known
Integral calculus and Differential calculus perform inverse operation they are just opposite to each other
Example Problems for Reviewing:
Integral Calculus Sample Problems for reviewing
Problem 1:
Find the integral of the given equation 6x2+18x dx
Solution:
?6x2+18x dx = ?6x2 dx +?18x dx
Integrating the above equation
We get
=6x3/3 + 18x2/2
Now simplifying the above equation we get
=2x3+ 9x2
Problem 2:
Integrate the following expression 2ex + 13ex .
Solution:
The expression is 2ex + 13ex
= ? 2ex+ 13 ex dx
= ? 2 ex dx + ? 13 ex dx
By integrating the above, we get as follows
= 2ex+ 13 ex + c.
Differential Calculus Sample Problems for reviewing
Find the gradient of
(I) the tangent (ii) the normal
To the curve y = 2x3 - 4x2 at the point (2, 3)
Solution:-
The given equation is y = 2x3 - 4x2
The given point (2, 3).
m1 = dy/dx
dy /dx = d/dx (2x3 - 4x2)
= 6x2 – 8x.
The slope of the tangent is dy/dx at x = 2
dy / dx at x = 2 is
dy/ dx = 6(2) 2 – 8(2)
= 24 – 16
m1 = 8
The slope of the normal is found using m1 × m2 = -1.
m1* m2 = -1
Plugging in the value of m1 in the m1 × m2 = -1.
We get
8 * m2 = -1
Now divide it by 8 on both sides
8 *m2 / 8= -1 / 8
m2 = - 1 / 8
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