Let f(x) = minimum (x+1,1−x) for all x≤1. Then the area bounded by y=f(x) and the x-axis is

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Let f(x) = minimum {({x}+{1},{{{1}-{x}}})} { for all } {x}{1}.

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Let f(x) = minimum $(x + 1, 1 - x) for all x \leq 1 .$ Then the area bounded by y=f(x) and the x-axis is

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Let f(x) = minimum

(x + 1, 1 - x) for all x \leq 1 .

Then the area bounded by y=f(x) and the x-axis is

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Practice questions from similar books

Question 1

The area bounded by the curve

y = x e^{- x}, y = 0 and x = c,

where c is the x-coordinate to the curve's inflection point, is

View solution

Question 2

Let A(k) be the area bounded by the curves

y = x^{2} - 3

and y=kx+2\displaystyle.

View solution

Question 3

If y=f(x) is a monotonic function in (a,b), then the area bounded by the ordinates at

x = a, x = b, y = f (x) and y = f (c) (where c \in (a, b)) is minimum when c = \frac{a + b}{2}

Proof : A = a \int c (f (c) - f (x)) d x + c \int b (f (c)) d x

= f (c) (c - a) - a \int c (f (x)) d x + a \int b (f (x)) d x - f (c) (b - c)

\Rightarrow A = [2 c - (a + b)] f (c) + c \int b (f (x)) d x - a \int c (f (x)) d x

Differentiating w.r.t. c, we get

\frac{d A}{d c} = [2 c - (a + b)] f^{'} (c) + 2 f (c) + 0 - f (c) - (f (c) - 0)

For maxima and minima ,

\frac{d A}{d c} = 0

\Rightarrow f^{'} (c) [2 c - (a + b)] = 0 (a s f^{'} (c) \neq = 0)

Hence,

c = \frac{a + b}{2}

Also for c < \frac{a + b}{2}, \frac{d A}{d c} < 0 and for c > \frac{a + b}{2}, \frac{d A}{d c} > 0

Hence, A is minimum when

c = \frac{a + b}{2}

.
If the area enclosed by

f (x) = sin x + cos x, y = a

between two consecutive points of extremum is minimum, then the value of a is

View solution

Question 4

The area of the region bounded by the curve

y = e^{x}

and lines x=0 and y=e is

View solution

Question Text

Let f(x) = minimum

(x + 1, 1 - x) for all x \leq 1 .

Then the area bounded by y=f(x) and the x-axis is

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Let f(x) = minimum (x+1,1−x​) for all x≤1. Then the area bounded by y=f(x) and the x-axis is

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Practice questions from similar books

Let f(x) = minimum $(x + 1, 1 - x) for all x \leq 1 .$ Then the area bounded by y=f(x) and the x-axis is