Substitution Method Calculus

Introduction
In this article we are going to discuss about the substitution method calculus problem concept. The process of short form the calculus corresponding to over screening the significant concept and problem in substitution method calculus are referred as review calculus. This article helps to improve the knowledge for using substitution method calculus problem and below the problems are helping toll for the exam. Go ahead of the test using review to this article. Substitution method calculus problem solutions also show below.

Level One Example Substitution Method Calculus Problems:-
Substitution method calculus problem 1:-

Integrals evaluated using the method of substitution:

`int sin (3x+5) dx`

Solution:-

Step 1:-

Let` u = 3x + 5`

Step 2:-

Then `du = 3dx`

Step 3:-

`int sin (3x + 5) dx = int sin (u)*(du)/ (3)`

`=1/3 int sin (u) du`

Step 4:-

`= 1/3 [- cos (u)] + C`

Step 5:-

`= 1/3 [- cos (3x+5)] + C`

Substitution method calculus problem 2:-

Integrals evaluated using the method of substitution:

`int (sqrt (7x-3)) dx`

Solution:-

Step 1:-

Let `u = 7x -3`

Step 1:-

Then `du = 7 dx`

Step 2:-

`int (sqrt (7x-3)) dx = int u^ (1/2) (du)/ (7)`

`= 1/7 int u^ (1/2) (du)`

Step 3:-

`= 1/7 u^ (3/2)/ (3/2) + C`

Step 4:-

`= 2/21 (7x - 3) ^ (3/2) +C.`

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Level Two Example Substitution Method Calculus Problems:-
Substitution method calculus problem 1:-

Integrals evaluated using the method of substitution:

`int 9 x e^ (5 - 3x^2) dx`

Solution:-

Step 1:-

Let` u = 5 - 3 x^2`

Step 2:-

Then` du = -6 x dx.`

Step 3:-

`int9 x e^ (5-3x^2) dx = int 9 e^ (5-3x^2) x dx`

`= int 9 e^u (du)/ (-6)`

Step 4:-

`= (-3)/ (2) int e ^u du`

`= (-3)/ (2) e^u + C`

Step 5:-

`= (-3)/ (2) e^ (5-3x^2) + C`

Substitution method calculus problem 2:-

Integrals evaluated using the method of substitution:

`int sin (5x) cos (5x) dx`

Solution:-

Step 1:-

Let `u = sin (5x)`

Step 2:-

Then `du = cos (5x) 5 dx.`

Step 3:-

`int sin (5x) cos (5x) dx = int u (du)/ (5)`

`= 1/5 int u du`

Step 4:-

`= 1/5 (u^2)/ (2) + C`

`= (1)/ (10) sin^2 (5x) + C.`