Q3.The area bounded by the curve y = 2x - x2 and the line x + y = 0 is
Answer : Option DExplaination / Solution: The equation y = 2x−x2 i.e.y−1=−(x−1)2represents a downward parabola with vertex at ( 1, 1 ) which meets x – axis where y = 0 .i .e . where x = 0 , 2. Also , the line y = - x meets this parabola where – x = 2x−x2 i.e. where x = 0 , 3. Therefore , required area is :
The area bounded by the curves y=x−−√,2y+3=xand the x- axis in the first quadrant is
Answer : Option AExplaination / Solution: To find area the curves y = x−−√ and x = 2y + 3 and x – axis in the first quadrant., We have ; y2−2y−3=0,( y – 3 ) ( y + 1) = 0 . y = 3 , - 1 . In first quadrant , y = 3 and x = 9. Therefore , required area is ;
Answer : Option AExplaination / Solution: The tangents are y=mx+am,y=mx+12m,since a=12. It passes through ( -2 , 0 ). ∴4m2=1⇒m=±12 The tangents are : y=x2+1,y=−x2−1 Required area :