AREA UNDER CURVE

1. Theareaboundedbythecurvesy=f(x), thexaxisandtheordinatesx=1andx=bis(b1)sin(3b+4).Thenf(x)is

(A)(x1)cos(3x+4) (B)sin(3x+4)(C)sin(3x+4)+3(x1)cos(3x+4) (D)noneofthese

2. The areaboundedby theparabolas y= (x+ 1)2 andy= (x 1)2 and the liney= 1/4 is(A)4sq.units (B)1/6sq.units (C)4/3sq.units (D)1/3sq.units

3. Theareaoftheregionenclosedbythecurvesy=xlogxandy=2x2x2is

(A)127

(B)21

(C)125

(D)noneofthese

4. Theareaoftheregionformedby xy,012y4x6yx 22 + - - + and25

x is

(A)8

136

+ -

p(B)

813

6 -

+ p

(C)8

136

- -

p(D)noneofthese

5. Areaboundedbythecurvexy2=a2(ax)andyaxisis

(A)2a2 p

(B) 2a p (C) 2a3p (D) 2a3 2 p

6. LetAnbetheareaboundedbythecurvey=(tanx)nandthelinesx=0,y=0andx= p / 4 .Prove

that for n > 2,An+A

n 2= 1/(n 1) and deduce that 1/(2n + 2)

10. LetC1andC

2bethegraphofthefunctionsy=x2and

y = 2x, 0 1 x respect ively. Let C3 be thegraphofafunctiony=f(x), 0 1 x ,f(0)=0.Forapoint P and C

1, let the lines t hrough P,

parallel to the axes, meet C2and C

3at Q and R

respectively.IfforeverypositionofP(onC1), the

areasoftheshadedregionsOPQandORPareequal,determinethefunctionf(x).

ANSWERKEY

1. C 2. D 3. A 4. C

5. B

7. 17/27sq.units 8. b=1 9. 2 3

10. f(x)=x3x2