Securing Higher Grades Costing Your Pocket? Book Your Assignment At The Lowest Price Now!

- +
250 Words
Upload File

    Inverse Chain Rule Method


    We solve the mathematicsintegral by using inverse chain rule method. Inverse chain rule method is very useful to integrate the function if given function in this form integral of [f(x)]^n f’(x). In order to integration by using inverse chain rule method we should be noticed that integrand consist of the product of derivative f’(x) of f(x) and should be a power of a function f(x).Then we find integral by increasing exponent unity and divide by increased index. Let us see the formula of integration by using inverse chain rule: - integral of [f(x)]^n * f’(x) = [f(x)]^n+1 / (n + 1), here n is not equal to -1.

    Let us see some examples of integration by using inverse chain rule method h(x) = (4x^4 + 2x^3 + 5x^2 + x + 1)^8 * (16x^3 + 6x^2 + 10x + 1). Solution: - Given function h(x) = (4x^4 + 2x^3 + 5x^2 + x + 1)^8 * (16x^3 + 6x^2 + 10x + 1). Here we let f(x) = 4x^4 + 2x^3 + 5x^2 + x + 1 then f’(x) = 16x^3 + 6x^2 + 10x + 1. We see that given integral in this form [f(x)]^n * f’(x). So that integration of h(x) = (4x^4 + 2x^3 + 5x^2 + x + 1)^8 * (16x^3 + 6x^2 + 10x + 1), using formula integral of [f(x)]^n * f’(x) = [f(x)]^n+1 / (n + 1), let us take integration and gate, Integral of (4x^4 + 2x^3 + 5x^2 + x + 1)^8 * (16x^3 + 6x^2 + 10x + 1) = (4x^4 + 2x^3 + 5x^2 + x + 1)^9 / 9 + C, here C is any constant..

    By using integration inverse chain rule, we can integrate difficult integration easily. Let we see another example: -find integration of sin^5 x * cos x by using inverse chain rule method.Solution: - Given integral function sin^5 x * cos x, Here we take f(x) = sinx then f’(x) = cosx. Now we can write in this form of f(x) ^n f’(x). So we use fomula integration by inverse chain rule ` integral of [f(x)]^n * f’(x) = [f(x)]^n+1 / (n + 1). Now bu using this formula integral function sin^5 x * cos x = sin^6 x / 6 + C, here C is any constant. Let we see another example: - Find the integration by using chain rule method if h(x) = (3x + 1) / (x^3 + x + 4). Solution: - Given function h(x) = (3x^2 + 1) / (x^3 + x + 4), Here we let f(x) = x^3 + x + 4, now f’(x) = 3x^2 + 1, So we use formula and gate Integral of (3x + 1) / (x^3 + x + 4) = log (x^3 + x + 4) + C.

    This is how the inverse chain rule can used. The illustrations stated above shows the steps of finding the integration of any function byusing the chain rule method.

    Our Amazing Features

    • On Time Delivery

    • Plagiarism Free Work

    • 24 X 7 Live Help

    • Services For All Subjects

    • Best Price Guarantee

    Live Reviews

    Ashley 02 Aug 2021

    I was not able to concentrate on academics and co-curricular activities all at once and hence I decided to seek professional assistance. The expert writers took care of my essay report so well as if it was their own. So no complaints at all!

    IOT 02 Aug 2021

    The service solution is extremely flexible that helps students to procure services anytime as they need one. I could connect to them at any time of the day which made me feel calm and relaxed.

    Ariella 02 Aug 2021

    My parents have been really happy with my academic performance lately, and all thanks to the team offering excellent support and academic help. Easy availability and a true choice of students around the world!

    Norah 02 Aug 2021

    I got a bonus mark this semester due to offering an error-free thesis. My examiner was so impressed with my assignment that she offered me a bonus mark which further boosted my grade.

    View All Reviews