wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Draw a rough sketch of the curve, y=x2+3x+2x23x+2 and find the area of the bounded region between the curve and x-axis.

Open in App
Solution

f(x)=(x+1)(x+2)(x1)(x2)
Graph will cut x-axis at x=1 and x=2
It is discontinuous at x=1 and x=2.
limxf(x)1, limx1f(x)+

limx1+f(x)

limx2f(x)

limx2+f(x)+, f(0)=1.

Now we have to find the area of the shaded region. The required area
=12f(x)dx=12(x2+3x+2x23x+2)dx=121+6x(x1)(x2)dx

=∣ ∣[x12+612(2x21x1)dx]∣ ∣

=[1+6[2 ln|x2|ln|x1|]12

=1+6[2(ln 3ln 4)(ln 2ln 3)]

=1+6[3 ln 35 ln 2]

=6 ln(3227)1 sq. units.

1635103_867554_ans_e01280027874454998ad3c31162e770e.JPG

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Functions
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon