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Improper Integrals

The area boun...

Question

The area bounded by curves y = e^x, y = e^–x and x axis, in square units, is

वक्रों y = e^x, y = e^–x तथा x-अक्ष द्वारा परिबद्ध क्षेत्र का क्षेत्रफल वर्ग इकाई में है

A

2e

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B

2

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C

e²

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D

2e²

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Solution

The correct option is B 2
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Q. The area bounded by the curve y = sinx and x-axis between x = 0 and x = π is (in sq. units)

x = 0 तथा x = π के मध्य वक्र y = sinx तथा x-अक्ष द्वारा परिबद्ध क्षेत्र का क्षेत्रफल है (वर्ग इकाई में)

Q. The area of the region bounded by parabola y² = 8x and its latus rectum in square units, is

परवलय y² = 8x तथा इसके नाभिलम्ब द्वारा परिबद्ध क्षेत्र का क्षेत्रफल वर्ग इकाई में है

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

Let the area bounded by x = –1, x-axis, y-axis and f(x) = 1 + x² be A₁ and the area bounded by x = 1, x-axis, y-axis and f(x) = 1 + x² be A₂ then

माना x = –1, x-अक्ष, y-अक्ष तथा f(x) = 1 + x² द्वारा परिबद्ध क्षेत्रफल A₁ है तथा x = 1, x-अक्ष, y-अक्ष व f(x) = 1 + x² द्वारा परिबद्ध क्षेत्रफल A₂ है, तब

Q. Line x + y = 5 intersect the x-axis and y-axis at F and G respectively and line x + y = –5 intersect the x-axis and y-axis at H and E respectively. Also, lines x = y = –5 intersect at A, lines x = –y = 5 intersect at B, lines x = y = 5 intersect at C and lines x = –y = –5 intersect at D. The difference of areas of squares ABCD and EFGH (in square units) is

रेखा x + y = 5, x-अक्ष व y-अक्ष को क्रमशः F तथा G पर प्रतिच्छेद करती है तथा रेखा x + y = –5, x-अक्ष व y-अक्ष को क्रमशः H तथा E पर प्रतिच्छेद करती है। इसी प्रकार, रेखाएँ x = y = –5, A पर प्रतिच्छेद करती है, रेखाएँ x = –y = 5, B पर प्रतिच्छेद करती है, रेखाएँ x = y = 5, C पर प्रतिच्छेद करती है तथा रेखाएँ x = –y = –5, D पर प्रतिच्छेद करती है। तब वर्ग ABCD तथा EFGH के क्षेत्रफलों (वर्ग इकाई में) का अन्तर है

Q. Area bounded by the curves

y = e^{x}, y = e^{- x}

and the straight line

x = 1

is (in sq units)

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