1. Calculate the following integral. Shows your steps and reasoning. (4) In z [ I -dz...

 

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1. Calculate the following integral. Shows your steps and reasoning. (4) In z [ I -dz 2. Calcluate the slope of this parametric curve. Identity any vertical tangents by finding places where the slope approaches infinity. (4) y(t) = (3t-t-1,t + 2t+4) 3. Calcluate the slope of this parametric curve. Identity any vertical tangents by finding places where the slope approaches infinity. (4) r(t) = ( 1 1 1 " t t 4. Calculate the length of this parametric curve. (4) y(t) = (5t-1,3t - 2) t = [0, 10] 5. Calculate the length of this parametric curve. (4) y(t) = (9t, t) t [0, 2] For the resulting integral, you can use this antiderivative instead of doing all of the work of a trig substitution. bt a +6+ +62 In + a a + btdt = 1/2 v 64 a +1+c The result you will get from this integral will be a complicated expression with square roots and logarithms. Leave your answer in this form; do not change it into decimals. 1. Calculate the following integral. Shows your steps and reasoning. (4) In z [ I -dz 2. Calcluate the slope of this parametric curve. Identity any vertical tangents by finding places where the slope approaches infinity. (4) y(t) = (3t-t-1,t + 2t+4) 3. Calcluate the slope of this parametric curve. Identity any vertical tangents by finding places where the slope approaches infinity. (4) r(t) = ( 1 1 1 " t t 4. Calculate the length of this parametric curve. (4) y(t) = (5t-1,3t - 2) t = [0, 10] 5. Calculate the length of this parametric curve. (4) y(t) = (9t, t) t [0, 2] For the resulting integral, you can use this antiderivative instead of doing all of the work of a trig substitution. bt a +6+ +62 In + a a + btdt = 1/2 v 64 a +1+c The result you will get from this integral will be a complicated expression with square roots and logarithms. Leave your answer in this form; do not change it into decimals.