Pre-Calc Homework Solutions 250

Pre-Calc Homework Solutions 250 - 250 Section 6.3 x ln x x...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: 250 Section 6.3 x ln x x 1 4. The graph of y2 of the graph of y1 x appears to be a vertical shift 9. dy dx x (x sin x sin x)dx ln t dt (down 1 unit). Thus, y2 dy appears to be an antiderivative of ln x which supports x ln x ln x. x C as the set of all antiderivatives of Integrate both sides. dy y y(0) 1 2 x 2 (x sin x) dx cos x C 2 3 3 1 C C y 10. 1 2 x 2 cos x [0, 6] by [ 2, 5] d 1 x e (sin x dx 2 1 x e (cos x 2 1 x e cos x 2 cos x) sin x) 1 x e sin x 2 (sin x cos x) e x 1 x e sin x 2 1 2 1 x e cos x 2 Quick Review 6.3 1. dy dx e x sin x (sin 2x)(3x 2) (x 3)(cos 2x)(2) 2x 3 cos 2x Section 6.3 Exercises 1. Let u x dx x cos x x cos x d Check: ( x cos x dx 3x 2 sin 2x ln (3x 1)(2e 2x) 1) dv v sin x dx cos x cos x dx sin x C C) (cos x)( 1) cos x 2. dy dx (e 2x) 3 du 3x 1 3e 2x 2e 2x ln (3x 3x 1 1 1 (2x)2 2 1 4x 2 1 1 (x 1 x sin x dx dy 3. dx 2 sin x ( x)( sin x) x sin x 3) 2 4. 5. dy dx y tan y x tan 3x 3x 2. Let u du x2 2x dx x 2 sin x dv v cos x dx sin x 2 x sin x dx 1 tan y 3 x 2 cos x dx 6. y cos y x 1 cos 1 (x 1) x 1 cos y 1 1 1 1 1 Using the result from Exercise 1, x 2 sin x 2x cos x 0 2[ x cos x (x 2 2)sin x (x 2 sin x] C 2)sin x (x 2 C 7. 0 sin x dx cos x cos ( 1) 1 1 d Check: [2x cos x dx C] 2)(cos x) cos 0 2 (2x)( sin x) (2 cos x)(1) (sin x)(2x) x 2 cos x 8. dy dx e 2x e 2x dx dy Integrate both sides. dy y e 2x dx 1 2x e 2 C ...
View Full Document

Ask a homework question - tutors are online