09%20-%20Integral%20Calculus

09%20-%20Integral%20Calculus - 9 - INTEGRAL CALCULUS Page 1...

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Unformatted text preview: 9 - INTEGRAL CALCULUS Page 1 ( Answers at the end of all questions ) ( 1 ) If I 1 = ∫ 1 2 x dx 2 , I 2 = ∫ 1 3 x dx 2 , I 3 = ∫ 2 1 2 x dx 2 , I 4 = ∫ 2 1 3 x dx 2 , then ( a ) I 2 > I 1 ( b ) I 1 > I 2 ( c ) I 3 = I 4 ( d ) I 3 > I 4 [ AIEEE 2005 ] ( 2 ) The area enclosed between the curve y = log e ( x + e ) and the coordinate axes is ( a ) 1 ( b ) 2 ( c ) 3 ( d ) 4 [ AIEEE 2005 ] ( 3 ) The parabolas y 2 = 4x and x 2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S 1 , S 2 , S 3 are respectively the area of these parts numbered from top to bottom, then S 1 : S 2 : S 3 is ( a ) 1 : 2 : 1 ( b ) 1 : 3 : 1 ( c ) 2 : 1 : 2 ( d ) 1 : 1 : 1 [ AIEEE 2005 ] ( 4 ) dx ) x log ( 1 ) 1- x log ( 2 2 ∫ + is equal to ( a ) c 1 ) x log ( x log 2 + + ( b ) c 1 x x 2 + + ( c ) c x 1 xe 2 x + + ( d ) c 1 ) x log ( x 2 + + [ AIEEE 2005 ] ( 5 ) Let f ( x ) be a non-negative continuous function such that the area bounded by the curve y = f ( x ), X-axis and the ordinates x = 4 π and x = β > 4 π is ( β sin β + 4 π cos β + 2 β ). Then f ( 2 π ) is ( a ) 4 π + 2 -1 ( b ) 4 π- 2 + 1 ( c ) 1 - 4 π- 2 ( d ) 1 - 4 π + 2 [ AIEEE 2005 ] ( 6 ) The value of dx a 1 x cos x 2 ∫ π π +- , a > 0 is ( a ) a π ( b ) 2 π ( c ) a π ( d ) 2 π [ AIEEE 2005 ] 9 - INTEGRAL CALCULUS Page 2 ( Answers at the end of all questions ) ( 7 ) ∑ = ∞ → n 1 r n r n e lim is ( a ) e ( b ) e - 1 ( c ) 1 - e ( d ) e + 1 [ AIEEE 2004 ] ( 8 ) If dx x ( sin x sin ) ∫ α- = Ax + B log sin ( x - α ) + C, then the value of ( A, B ) is ( a ) ( sin α , cos α ) ( b ) ( cos α , sin α ) ( c ) ( - sin α , cos α ) ( d ) ( - cos α , sin α ) [ AIEEE 2004 ] ( 9 ) x sin x cos dx ∫- is equal to ( a ) C 8 2 x tan log 2 1 + π- ( b ) C 2 x cot log 2 1 + ( c ) C 8 3 2 x tan log 2 1 + π- ( d ) C 8 3 2 x tan log 2 1 + π + [ AIEEE 2004 ] ( 10 ) The value of dx x 1 3 2 2 ∫-- is ( a ) 3 28 ( b ) 3 14 ( c ) 3 7 ( d ) 3 1 [ AIEEE 2004 ] ( 11 ) The value of I = dx 2x sin 1 ) x cos x sin ( 2 2 ∫ π + + is ( a ) 0 ( b ) 1 ( c ) 2 ( d ) 3 [ AIEEE 2004 ] ( 12 ) If ∫ π dx ) x sin ( f x = A ∫ π 2 dx ) x sin ( f , then A is equal to ( a ) 0 ( b ) π ( c ) 4 π ( d ) 2 π [ AIEEE 2004 ] 9 - INTEGRAL CALCULUS Page 3 ( Answers at the end of all questions ) ( 13 ) If f ( x ) = x x e 1 e + , 1 I = ∫ ) a ( f ) a ( f dx } ) x 1 ( x { g x-- and 2 I = ∫ ) a ( f ) a ( f dx } ) x 1 ( x { g-- , then the value of 1 2 I I is ( a ) 2 ( b ) - 3 ( c ) - 1 ( d ) 1 [ AIEEE 2004 ] ( 14 ) The area of the region bounded by the curves y = l x - 2 l, x = 1, x = 3 and X-axis is ( a ) 1 ( b ) 2 ( c ) 3 ( d ) 4 [ AIEEE 2004 ] ( 15 ) The value of x sin x dt t sec...
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This note was uploaded on 11/28/2011 for the course MATH 300 taught by Professor Jones during the Spring '06 term at ITT Tech Flint.

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09%20-%20Integral%20Calculus - 9 - INTEGRAL CALCULUS Page 1...

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