Question
Integration Prep
- Find
(accessible to students on the path to grade 3 or 4) [6 marks]
- Do not use a calculator to answer this question.
Find the exact value of
.
(accessible to students on the path to grade 3 or 4 ) [5 marks]
- The diagram shows the graph of
. Find the value of
such that the shaded area equals 6.8 .
(accessible to students on the path to grade 3 or 4) [6 marks]
Find the exact value of
(accessible to students on the path to grade 3 or 4 ) [5 marks]
Ask by Cruz Phillips. in Switzerland
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
-
The integral of
with respect to is . -
The exact value of
is . -
The value of
such that the shaded area under from to equals is approximately .
Solution

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Mind Expander
To tackle the first integral, we can rewrite the expression
to make things easier. This becomes
. Now let’s write it in terms of
powers:
. Integrating gives us
.
For the definite integral
, we first find the antiderivative of
, which is
. Evaluating from
to
, we compute
. Since
, we get
.
As for the value of
in the equation
such that the shaded area equals 6.8, it’s useful to set up the integral
. This gives us the area under the curve from
to
. You would typically need to find where this integral equals 6.8, which may involve numerical methods or a graphing approach since there isn’t a simple antiderivative for
that can be worked out directly.
So, get ready to roll up your sleeves and dive into those integrals! They’ll take some practice, but you’ll get the hang of it before you know it!