is this one question or 5 distinctive ones? a number of them look soliciting for the quintessential of |t| with admire to t from -4 to eight, others look soliciting for the quintessential of |t| from -2 to 4. Is the two of those the question you're attempting to ask? To combine an absolute fee, chop up the quintessential into parts under 0 and parts above 0. provided that |t| = t whilst t >= 0, and |t| = -t whilst t < 0, then you definately can say quintessential(-4,8) |t| dt = quintessential(-4,0) |t| dt + quintessential(0, 8) |t| dt = quintessential(-4,0) (-t) dt + quintessential(0, 8) t dt And the two a sort of only contain integrating t dt, which you ought to be attentive to the thank you to do.
Obviously you recognize the problem of integrating the absolute value of t. The way to deal with this is to split is between when t is negative and when it is positive.
So
8
∫.....|t| dt =
-4
0
∫.....(-t) dt
-4
+
8
∫.....(t) dt
0
Here we change |t| to (-t) on the interval where t is negative because |t| = (-t) if t is negative.
Obviously |t| = (t) if t is positive.
Do both integrals and add them up and it'll sork out for you.
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is this one question or 5 distinctive ones? a number of them look soliciting for the quintessential of |t| with admire to t from -4 to eight, others look soliciting for the quintessential of |t| from -2 to 4. Is the two of those the question you're attempting to ask? To combine an absolute fee, chop up the quintessential into parts under 0 and parts above 0. provided that |t| = t whilst t >= 0, and |t| = -t whilst t < 0, then you definately can say quintessential(-4,8) |t| dt = quintessential(-4,0) |t| dt + quintessential(0, 8) |t| dt = quintessential(-4,0) (-t) dt + quintessential(0, 8) t dt And the two a sort of only contain integrating t dt, which you ought to be attentive to the thank you to do.
Obviously you recognize the problem of integrating the absolute value of t. The way to deal with this is to split is between when t is negative and when it is positive.
So
8
∫.....|t| dt =
-4
0
∫.....(-t) dt
-4
+
8
∫.....(t) dt
0
Here we change |t| to (-t) on the interval where t is negative because |t| = (-t) if t is negative.
Obviously |t| = (t) if t is positive.
Do both integrals and add them up and it'll sork out for you.