{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assignment4bfsol

# assignment4bfsol - ma2176 a4 Brief Sol Integration and its...

This preview shows pages 1–3. Sign up to view the full content.

1 ma2176 a4 Brief Sol Integration and its Applications 1. Let + < = 2 1 if 2 1 0 if 3 ) ( x x x x x f . Find 2 0 , ) ( ) ( 0 = x dt t f x F x . Solution : For 1 0 < x , ( ) ( ) 2 0 0 ( ) 3 3 2 x x x F x f t dt t dt x = = = . For 2 1 x , ( ) ( ) ( ) ( ) 1 1 2 0 0 1 0 1 ( ) 3 (2 ) 2 . 2 x x x x F x f t dt f t dt f t dt t dt t dt x = = + = + + = + 2. Evaluate the following integrals: (a) dx x x + 1 (b) dx x x + 2 2 1 (c) dx e e x x + + 1 1 3 Solution : (a) C x x dx x x dx x x + + = + = + 2 3 2 1 1 2 3 (b) 2 2 2 1 1 arctan 1 1 x dx dx x x C x x = = + + + (c) ( ) ( )( ) ( ) 3 2 3 2 2 1 1 1 1 1 1 1 1 2 x x x x x x x x x x x x e e e e e e dx dx dx e e dx e x C e e e + + + + = = = + = + + + + + 3. Evaluate the following integrals: (a) dx x x 1 2 (b) ( ) dx x x + 1 0 10 2 1 (c) ( ) 1 0 2 1 x x dx + + (d) 4 3 0 sin (2 )cos(2 ) x x dx π (e) dx x x 2 1 (f) dx x tan Solution : (a) ( ) ( ) 3 2 2 2 2 2 1 1 1 1 1 1 2 3 x x dx x d x x C = = + (b) ( ) ( ) ( ) ( ) 1 1 10 10 2 2 2 11 0 0 1 1 1 1 1 2 1 2 22 x x dx x d x + = + + = (c) ( ) 1 1 1 0 0 0 1 1 2 1 2 1 (2 1) 3 2 3 x x dx xdx x d x + + = + + + = +

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

View Full Document
2 (d) ( ) 4 4 3 3 0 0 1 1 sin (2 )cos(2 ) sin (2 ) sin(2 ) 2 8 x x dx x d x π π = = (e) ( ) ( ) ( ) 1 1 2 2 2 2 2 2 1 1 1 1 2 1 x dx x d x x C x = − = − + (f) sin (cos ) tan ln cos cos cos x d x xdx dx x C x x = = − = − + 4. Evaluate the following integrals by integration by parts: (a) dx xe x (b) xdx x 2 sin 2 (c) xdx arcsin Solution : (a) ( ) x x x x xe dx xd e xe e C = = − + (b) 2 2 2 2 2 cos(2 ) cos(2 ) cos(2 ) sin(2 ) sin(2 ) cos(2 ) 2 2 2 2 cos(2 ) sin(2 ) cos(2 ) 2 2 4 x x x x x x x x x x d x x dx xd x x x x x C = = − + = − + = − + + +
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

assignment4bfsol - ma2176 a4 Brief Sol Integration and its...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online