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Example1

Title: Calculus

Grade Lesson s6-p2

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

Evaluate the integral \$ \int (2x + 1)/(x^2) dx \$.

Step: 1

We can rewrite the integrand as:

\$ (2x + 1) / (x^2) = (2x)/(x^2) + 1/(x^2) = 2/x + 1/(x^2)\$

Splitting the integral, we get:

\$ \int 2/x dx + \int 1/(x^2) dx\$

Explanation:

Here, we rewrote and split the integrand.

Step: 2

The integration formulas are:

\$ \int 1/x dx = ln | x | + c, \int x^n dx = (x^(n+1))/(n+1) + c \$

Now applying the formulas we get:

\$ 2 \int (1/x) dx + \int (x^(-2)) dx \$

After integration, we get:

\$ 2 ln | x | + (x^(-2 + 1))/(-2 + 1) + c \$

After simplification :

\$ 2 ln | x | + (x^(-1))/(-1) + c \$

\$ 2 ln | x | - 1/x + c \$

Explanation:

Here, after applied the formulas then we get \$ 2 ln | x | - 1/x + c \$