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Question

Mathematics Question on Integral Calculus

Which of the following is/are TRUE ?

A

0101𝑒max(𝑥2,𝑦2)𝑑𝑥𝑑𝑦=𝑒1∫^1_0 ∫^1_0 𝑒^{ max}(𝑥 ^2 , 𝑦^ 2) 𝑑𝑥\,\, 𝑑𝑦 = 𝑒 − 1

B

0101𝑒min(𝑥2,𝑦2)𝑑𝑥𝑑𝑦=01𝑒𝑡2𝑑𝑡(𝑒1)∫^1_0 ∫^1_0 𝑒^{ min}(𝑥 ^2 , 𝑦^ 2) 𝑑𝑥\,\, 𝑑𝑦 = ∫ ^1_0𝑒^{ 𝑡^ 2} 𝑑𝑡 − ( 𝑒 − 1)

C

0101𝑒max(𝑥2,𝑦2)𝑑𝑥𝑑𝑦=201y1𝑒𝑡2dxdy∫^1_0 ∫^1_0 𝑒^{ max}(𝑥 ^2 , 𝑦^ 2) 𝑑𝑥\,\, 𝑑𝑦 = 2∫ ^1_0∫ ^1_y𝑒^{ 𝑡^ 2} \,dx\,dy

D

0101𝑒max(𝑥2,𝑦2)𝑑𝑥𝑑𝑦=2011y𝑒y2dxdy∫^1_0 ∫^1_0 𝑒^{ max}(𝑥 ^2 , 𝑦^ 2) 𝑑𝑥\,\, 𝑑𝑦 = 2∫ ^1_0∫ ^y_1𝑒^{ y^ 2} \,dx\,dy

Answer

0101𝑒max(𝑥2,𝑦2)𝑑𝑥𝑑𝑦=𝑒1∫^1_0 ∫^1_0 𝑒^{ max}(𝑥 ^2 , 𝑦^ 2) 𝑑𝑥\,\, 𝑑𝑦 = 𝑒 − 1

Explanation

Solution

The correct options are: A and C