Compute the following integral: ∫ ( 5 t 2 − 1 + 4 t 2 ) d t {“version”:”1.1″,”math”:”\int\left(\frac{5}{t^2}-1+4t^2\right)\,dt”} Select an option from below:

Compute the following integral: ∫ sec ⁡ θ ( tan ⁡ θ + sec ⁡ θ + cos ⁡ θ ) d θ {“version”:”1.1″,”math”:”\int\sec\theta(\tan\theta+\sec\theta+\cos\theta)\,d\theta”} Select an option from below:

This last question culminates the exercise to connect the Riemann sum and the Fundamental Theorem of Calculus (3/3): Use the Fundamental Theorem of Calculus to check your answer from the previous question, question 7: f ( x ) = x 3 + 1 {“version”:”1.1″,”math”:”f(x)=x^3+1″}for 0 ≤ x ≤ 3. Select an option from below:

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(1 point) A circular idler shaft has a single gear at its center, which exerts a force of 45 lbs on the shaft.  What is the maximum critical speed of the shaft due to this external loading? Use Dunkerley’s equation for estimating the critical speed. Report your answer in revolutions per minute to one decimal place. The shaft characteristics are as follows: Length – 20 in; Diameter – 1in; Young’s Modulus – 30,000 kpsi; Specific mass,

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Compute the following integral: ∫ 0 1 y ( y 2 + 1 ) 5 d y {“version”:”1.1″,”math”:”\int_0^1 y(y^2+1)^5\,dy”} Select an option from below:

A car starting at rest accelerates at 16 ft/s² for 5 seconds on a straight road. How far does the car travel during this time? Select an option from below:

Continuous improvement is usually not related to innovation.

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