wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

The area of the region bounded by the curve y=tanx, the tangent to the curve at x=π4 and the x-axis is

A
14(loge41)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
14(loge21)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12(loge41)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
12(loge21)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 14(loge41)

Slope of the tangent at x=π4 is sec2π4=2
Equation of the tangent at A is,
y1=2(xπ4)
Coordinates of B are (π412,0)
BC=12

Required area
= Area of OACO Area of ΔABC
=π/40tanx dx12×AC×BC
=[logesecx]π/4012×1×12=(loge20)14=14(loge41)

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Area under the Curve
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon