Evaluate the double integral. 7x sin y'dA; Ris the region that is bounded by y = x², y = -x', and y = 125. R Round your answer to five decimal places. 2sin i 1.90466

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A: A separable differential equation can be written is of the form of dydx=f(x)g(y).

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A: Topic:- derivatives

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A: Yes the statement is True, the substitution is the most convenient way to compute the integral

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A: The simplest approach to do this question is to verify through options.

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Q: 2. Find S +l" dudy by first snitching the order of integration 4

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Q: dx 2. x²V4-x?

A: Just use the trigonometrical substitution to make integral easy and then solved it.

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Q: 5. J 12 csc (-6х) cot (-6x) dx 6. J2x3 cot х4 dx 7. S xª sec (x5 - 9) dx 8. S tan 3 x dx

A: The given integral are 5) 12 csc(-6x) cot(-6x)  6) 2x3 cot(x4)

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A: answer is in next step . as per guideline i can only answer one question

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A: topic- differential equations

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A: Since multiple questions are asked,I am doing first question

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A: Topic:- application of integration

Q: Ty csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соfу+ coty dy D) None E у…

A: Integrate by parts.

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 은(1-x) 2+C

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A: Solved below.

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A: To solve the following differential equation

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A: To find the antiderivative of fx=52x.

Q: Find div F and curl F if F(x, y, z) = x’i – 7j + yzk. - div F= curl F=

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A: Solution:

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A: exy=e4x-e5yDifferentiate with respect to yyexy+xexydydx=-5e5ydydx(xexy+5e5y)dydx=-yexy

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A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

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