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# assignment4 - ma2176 a4 Integration and its Applications x...

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ma2176 a4 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 . 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 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 4. Evaluate the following integrals by integration by parts: (a) dx xe x (b) xdx x 2 sin 2 (c) xdx arcsin 5. Evaluate the following integrals by partial fractions: (a) 3 2 2 x dx x x + (b) + 1 3 x dx (c) + + 1 2 4 x x dx 6. Evaluate the following integrals: (a) dx x 2 2 2 1 (b) 2 0 ) ( dx x f , where < + = 2 1 2 1 0 2 ) ( x x x x x f (c) dx x x p q q p + 1 0 , where 0 , > q p 7. Find the area of the region cut from the first quadrant by the curve 2 1 2 1 2 1 a y x = + . 8. Find the area enclosed by the curve x y ln = , the tangent of this curve at
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