6.2_Integration_by_Substitution_summer

# 6.2_Integration_by_Substitution_summer - Replace u by g(x)...

This preview shows pages 1–6. Sign up to view the full content.

6.2 Integration by Substitution Warm-u[s from 6.1 Find the indefinite integral f(x) = ∫ (16x 3 + 5x – 7) dx Find an antiderivative: f(x) = 16/(23x) Find the indefinite integral f(x) = ∫ 16e x dx Find f(x) by solving the initial value problem f ‘(x) = 6 + e x and f(1) = 7 + e Canon Precision Instruments makes an automatic electronic flash. The estimated marginal profit associated with producing

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
and selling these flashes is -0.006x + 30 dollars/unit/month when the production level is x units per month. Cannon’s fixed costs for these flashes is \$17,000/month. What is the maximum monthly profit? 6.2 Integration by Substitution Let u = g(x) where g(x) is a part of the integrand, usually the “inside” function Find du which equals g’(x) dx Convert the entire integral into one containing only u and du by substitution Evaluate the resulting integral

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Replace u by g(x) to find the final solution as a function of x. Find the indefinite integral: (3x 2- 2x +1)(x 3- x 2 + x) 13 dx Find the indefinite integral: 2(11x+ 9) 5 dx Find the indefinite integral: x 6 (7x 7 + 3) 4 dx Find the indefinite integral: 8t 7 (t 8 + 5) (1/4) dt Find the function f given that the slope of the tangent line to the graph at any point (x, f(x) is f (x) and that the graph passes through (2,1) where f (x) = 3x 2 /(2 x 3- 7) Find the indefinite integral: ___5x 2 ___ dx (9 4x 3 ) Find the indefinite integral: e 8x dx Find the indefinite integral: ___e 6x ___ dx (3 + e 6x ) Find the indefinite integral: 3x 4 e (x^5 8) dx Find the indefinite integral: (ln x) 20 / x dx Find the indefinite integral: 12/[x(ln (x)) (38) ] dx...
View Full Document

## This note was uploaded on 10/07/2011 for the course MATH 1431 taught by Professor Vaughn during the Spring '08 term at LSU.

### Page1 / 6

6.2_Integration_by_Substitution_summer - Replace u by g(x)...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online