QUESTIONS ON INTEGRATION

# QUESTIONS ON INTEGRATION - a is completely immersed in...

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QUESTIONS ON INTEGRATION 1. Find the integral ( ) f x dx x . Then, produce MATLAB plots of the original function ) ( x f and of the function resulting from the integration process. a) x e x x x x f 2 4 / 3 3 ) 4 sin( 2 1 ) ( - + - + = b) ) 1 3 ln( 1 5 ) ( 3 / 2 + + + + = - x x x x f 2. Evaluate the integral of the following functions using integration by parts: a) 3 ) 5 ln( ) ( x x x f = b) 1 2 2 ) ( + = x e x x f 3. Evaluate the integral of the following function using partial fraction decomposition: 6 1 5 4 ) ( 2 2 3 - - + - + = x x x x x x f 4. Evaluate the following definite integrals:

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a) - + + + + = - - 5 2 3 / 4 / 1 2 ) 2 sin( 1 2 1 3 dx x e x x x I x b) dx xe I x =
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Unformatted text preview: a is completely immersed in fluid and located in a vertical plane with a vertex at a depth h below the surface of the fluid. The force F acting on one side of the plate is given by: dy y h y F a ∫-= 3 ) ( 3 2 ρ where ρ is the fluid density, while the total moment M is given by: dy y h y M a ∫-= 3 2 ) ( 3 2 Find the location of the centre of pressure y , given by: ) ( y h F M-=...
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