Asked by Mai
Explain how you would use the power integration formula to integrate the function f(x) = (1/x^2)-(1/x)+(1/4).
Answers
Answered by
drwls
Integrate each of the three terms separately, using what you call the "power integration formula", and add up the results.
The formula you are probably refering to is:
Integral of (a*x^n) = a*n*x^(n+1)/(n+1)
where a is the constant coefficient and n is the constant exponent.
1/4 can be thought of as (1/4)*x^0, so its integral is (1/4)*x^1/1 = x/4
The integral of the 1/x term is a special case, since you cannot divide by zero. Its integral is the natural logarithm of x, ln x
Now integrate the 1/x^2 term and add the integral results of all three terms. You can add an arbitrary constant at the end if you wish.
The final answer is
-1/x + ln x +x/4 + C
The formula you are probably refering to is:
Integral of (a*x^n) = a*n*x^(n+1)/(n+1)
where a is the constant coefficient and n is the constant exponent.
1/4 can be thought of as (1/4)*x^0, so its integral is (1/4)*x^1/1 = x/4
The integral of the 1/x term is a special case, since you cannot divide by zero. Its integral is the natural logarithm of x, ln x
Now integrate the 1/x^2 term and add the integral results of all three terms. You can add an arbitrary constant at the end if you wish.
The final answer is
-1/x + ln x +x/4 + C
Answered by
help
How do you integrate a radical function such as f(x)= ã(7&4x^5 )- 3ã(6&x^5 )- 11∜x +3∛x ? Describe your strategy.
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