1 ) / ( ₁ + ²x^²) = ( -da f (₁ () [ dr. - 2³-1 2+1 (d) 2² + 7x+12² (a) +at da. dr.

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A: solution ) ∫ ( t - t2 3 +t35 ) dt = ∫ ( t1/2 - t2/3 + t3/5 ) dt  we know that  ∫xn = xn+1/n+1  = (…

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Q: II. Evaluate the following integrals: 1 2. fg x + 3 dx 8x+3 1. dx f X 4. - X +1 1 ₂2x+7 7. ƒ (2+ In…

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Q: y=8x-x³ 12) Where is the function concave down?

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Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

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Q: 2 6) Compute the area bounded by y² + 2y + 4 and y = 4.

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A: Given dt=6tfor 0&lt;t≤133t+αfor 13&lt;t≤56βσfor 56&lt;t≤13123t+α2σfor 1312&lt;t≤116

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Q: solve xy' - y = xkyn, 1) y¹ – O a. (k+n O b. (k+n O c. (k+n O d. (k+n - - n 1) x¹ - n - 1) x¹ − n 1)…

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A: Given: Now,           y' +y=y2⇒dyy2-y=dtIntegrating both sides we get,⇒y=11-et+c1

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Q: + 22/12 =)₁ y x² + y² dx + (ye³ +2²4₁²) dy = 0 =)

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