Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 69

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IMPORTANT

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Area enclosed between the curve $y = \log_{e} (x + e)$ and the co-ordinate axes is

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Important Questions on Area under Curves

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 70

Area bounded by

y = f^{- 1} (x)

and tangent and normal drawn to it at the points with abscissa

π and 2 π

, where

f (x) = \sin x - x

is:

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 72

The area bounded by the curve

y = \sin^{2} x - 2 \sin x

and the

x

-axis, where

x \in [0, 2 π],

is:

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 73

Suppose

y = f (x)

and

y = g (x)

are two functions whose graphs intersect at the three points

(0, 4), (2, 2)

and

(4, 0)

with

f (x) > g (x)

for

0 < x < 2

and

f (x) < g (x)

for

2 < x < 4

. If

\int_{0}^{4} [f (x) - g (x)] d x = 10

and

\int_{2}^{4} [g (x) - f (x)] d x = 5

, the area between two curves for

0 < x < 2

, is:

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Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 74

The area bounded by the curves

y = |x| - 1

and

y = - |x| + 1

is (in sq. units)

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Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 75

The area under the curve

y = |\cos x - \sin x|, 0 \leq x \leq \frac{π}{2}

, and above

x -

axis is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 76

The area of the figure bounded by the curves $y = e^{x}$ , $y = e^{- x}$ and the straight line $x = 1$ is

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Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 77

The area of the region bounded by

x = 0, y = 0, x = 2, y = 2, y \leq e^{x}

and

y \geq \ln x

is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 30 - Area under Curves>Exercise 1>Q 78

Let

R

be the region containing the point

(x, y)

on the

X Y

-plane, satisfying

2 \leq |x + 3 y| + |x - y| \leq 4

. Then the area of this region is: